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An upper bound on the asymptotic translation lengths on the curve graph and fibered facesJan 20 2018We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(\Sigma_n, \psi_n)$ of fibers and ... More

Darboux charts around holomorphic Legendrian curves and applicationsFeb 02 2017Jun 16 2017In this paper, we find a holomorphic Darboux chart around any immersed noncompact holomorphic Legendrian curve in a complex contact manifold $(X,\xi)$. By using such a chart, we show that every holomorphic Legendrian immersion $R\to X$ from an open Riemann ... More

Hedgehogs for neutral dissipative germs of holomorphic diffeomorphisms of $(\mathbb{C}^{2},0)$Nov 28 2016We prove the existence of hedgehogs for germs of complex analytic diffeomorphisms of $(\mathbb{C}^{2},0)$ with a semi-neutral fixed point at the origin, using topological techniques. This approach also provides an alternative proof of a theorem of P\'erez-Marco ... More

The Franks-Misiurewicz conjecture for extensions of irrational rotationsNov 16 2016We show that a toral homeomorphism which is homotopic to the identity and topologically semiconjugate to an irrational rotation of the circle is always a pseudo-rotation (i.e. its rotation set is a single point). In combination with recent results, this ... More

On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotationsNov 11 2016We prove that any minimal $2$-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a consequence of this, ... More

On transfer operators on the circle with trigonometric weightsOct 24 2016We study spectral properties of the transfer operators $L$ defined on the circle $\mathbb T=\mathbb R/\mathbb Z$ by $$(Lu)(t)=\frac{1}{d}\sum_{i=0}^{d-1} f\left(\frac{t+i}{d}\right)u\left(\frac{t+i}{d}\right),\ t\in\mathbb T$$ where $u$ is a function ... More

Molino theory for matchbox manifoldsOct 12 2016A matchbox manifold is a foliated space with totally disconnected transversals, and an equicontinuous matchbox manifold is the generalization of Riemannian foliations for smooth manifolds in this context. In this paper, we develop the Molino theory for ... More

On some generalizations of skew-shifts on $\mathbb{T}^2$Oct 11 2016In this paper we investigate maps of the two-torus $\mathbb{T}^2$ of the form $T(x,y)=(x+\omega,g(x)+f(y))$ for Diophantine $\omega\in\mathbb{T}$ and for a class of maps $f,g:\mathbb{T}\to\mathbb{T}$, where each $g$ is strictly monotone and of degree ... More

Polynomial-time algorithms for the curve graphSep 29 2016Oct 04 2016We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can ... More

Decoupling of the Kontsevich-Zorich cocycle modulo $q$ and uniform spectral gapSep 18 2016Oct 14 2016We obtain a qualitative extension of Selberg's $3/16$ Theorem to the setting of moduli spaces of abelian differentials on genus $g \geq 2 $ surfaces. More precisely, under certain conditions we prove that there is a uniform spectral gap for the foliated ... More

Newton flows for elliptic functions III Classification of $3^{\text{rd}}$ order Newton graphsSep 05 2016A Newton graph of order $r( \geqslant 2)$ is a cellularly embedded toroidal graph on $r$ vertices, $2r$ edges and $r$ faces that fulfils certain combinatorial properties (Euler, Hall). The significance of these graphs relies on their role in the study ... More

Newton flows for elliptic functions II Structural stability: Classification & RepresentationSep 05 2016In our previous paper we associated to each non-constant elliptic function $f$ on a torus $T$ a dynamical system, the elliptic Newton flow corresponding to $f$. We characterized the functions for which these flows are structurally stable and showed a ... More

Newton flows for elliptic functions I Structural stability: Characterization & GenericitySep 05 2016Newton flows are dynamical systems generated by a continuous, desingularized Newton method for mappings from a Euclidean space to itself. We focus on the special case of meromorphic functions on the complex plane. Inspired by the analogy between the rational ... More

Stability of the rotation set of area-preserving toral homeomorphismsSep 05 2016We characterize the rotation sets for homeomorphisms of the two dimensional torus which have stable rotation sets under small perturbations, showing that they must be convex polygons with rational vertices. We also give explicit estimates on the rationals ... More

Hitting and escaping statistics: mixing, targets and holesSep 05 2016There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one can move through ... More

New pathways and connections in Number Theory and Analysis motivated by two incorrect claims of RamanujanAug 12 2016We focus on three pages in Ramanujan's lost notebook, pages 336, 335, and 332, in decreasing order of attention. On page 336, Ramanujan proposes two identities, but the formulas are wrong -- each is vitiated by divergent series. We concentrate on only ... More

Fixed point free homeomorphisms of the complex planeAug 09 2016Our purpose in this article is to prove that the group $H({\bf C})$ of homeomorphisms of the complex plane ${\bf C}$ is a metric group equipped with the metric induced by uniform convergence of homeomorphisms and their inverses on compacts and the set ... More

On polynomially integrable planar outer billiards and curves with symmetry propertyJul 26 2016We show that every polynomially integrable planar outer convex billiard is elliptic.

Fekete polynomials and shapes of Julia setsJul 18 2016We prove that a nonempty, proper subset $S$ of the complex plane can be approximated in a strong sense by filled Julia sets of polynomials of degree at least two if and only if $S$ is bounded and $\hat{\mathbb{C}} \setminus \textrm{int}(S)$ is connected. ... More

Characterizing meromorphic pseudo-lemniscatesJul 15 2016Let $f$ be a meromorphic function with simply connected domain $G\subset\mathbb{C}$, and let $\Gamma\subset\mathbb{C}$ be a smooth Jordan curve. We call a component of $f^{-1}(\Gamma)$ in $G$ a $\Gamma$-$pseudo$-$lemniscate$ of $f$. In this note we give ... More

Singular SRB measures for a non 1--1 map of the unit squareJul 06 2016We consider a map of the unit square which is not 1--1, such as the memory map studied in \cite{MwM1}. Memory maps are defined as follows: $x_{n+1}=M_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1}),$ where $\tau$ is a one-dimensional ... More

A decomposition theorem for singular spaces with trivial canonical class of dimension at most fiveJun 29 2016In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite ... More

Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effectJun 08 2016We investigate the asymptotic behaviour of a reduced {\alpha}{\Omega}-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the {\alpha}-effect results in a system with state-dependent stochastic perturbations. By computing ... More

Twisted Coxeter elements and Folded AR-quivers via Dynkin diagram automorphisms:IIJun 01 2016Jul 22 2016As a continuation of the previous paper, we find a combinatorial interpretation of Dorey's rule for type $C_n$ via twisted Auslander-Reiten quivers (AR-quivers) of type $D_{n+1}$, which are combinatorial AR-quivers related to certain Dynkin diagram automorphisms. ... More

Twisted Coxeter elements and folded AR-quivers via Dynkin diagram automorphisms: IMay 31 2016We introduce and study the twisted adapted $r$-cluster point and its combinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded AR-quivers, of type $A_{2n+1}$ which are closely related to twisted Coxeter elements and the non-trivial ... More

Twisted Coxeter elements and folded AR-quivers via Dynkin diagram automorphisms: IMay 31 2016Oct 27 2016We introduce and study the twisted adapted $r$-cluster point and its combinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded AR-quivers, of type $A_{2n+1}$ which are closely related to twisted Coxeter elements and the non-trivial ... More

The BMO-Dirichlet problem for elliptic systems in the upper-half space and quantitative characterizations of VMOMay 26 2016We prove that for any homogeneous, second order, constant complex coefficient elliptic system $L$, the Dirichlet problem in $\mathbb{R}^{n}_{+}$ with boundary data in BMO is well-posed in the class of functions $u$ with $d\mu_u(x',t):=|\nabla u(x',t)|^2\,t\,dx'dt$ ... More

Automatically generating Fukaya categories and computing quantum cohomologyMay 25 2016Jun 29 2016Suppose one has found a non-empty sub-category $\mathcal{A}$ of the Fukaya category of a compact Calabi-Yau manifold $X$ which is homologically smooth in the sense of non-commutative geometry, a condition intrinsic to $\mathcal{A}$. Then, we show $\mathcal{A}$ ... More

A Framework for FFT-based Homogenization on Anisotropic LatticesMay 18 2016Jun 21 2016In order to take structural anisotropies of a given composite and different shapes of its unit cell into account, we generalize the Basic Scheme in Homogenization by Moulinec and Suquet to arbitrary sampling lattices and tilings of the d-dimensional Euclidean ... More

Anosov representations and dominated splittingsMay 05 2016We provide a link between Anosov representations introduced by Labourie and dominated splitting of linear cocycles. This allows us to obtain equivalent characterizations for Anosov representations and to recover recent results due to Gu\'eritaud-Guichard-Kassel-Wienhard ... More

Discrepancy of second order digital sequences in function spaces with dominating mixed smoothnessApr 29 2016Aug 24 2016The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the BMO and exponential Orlicz norms, as ... More

Statistical and Deterministic Dynamics of Maps with MemoryApr 24 2016We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha)\cdot x_{n-1}),$ where $\tau$ is ... More

Lifts of pseudo-Anosov homeomorphisms of nonorientable surfaces have vanishing SAF invariantApr 19 2016Aug 03 2016We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.

On the structure of the two-stream instability -- complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modesApr 11 2016The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species based on a 1D warm-fluid model, the instability diagram ... More

Minkowski dimension and explicit tube formulas for $p$-adic fractal stringsMar 30 2016The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a $p$-adic fractal ... More

On the exponent of the automorphism group of a compact Riemann surfaceMar 22 2016Oct 03 2016Let $X$ be a compact Riemann surface of genus $g\geq 2$, and let $Aut(X)$ be its group of automorphims. We show that the exponent of $Aut(X)$ is bounded by $42(g-1)$. We also determine explicitly the infinitely many values of $g$ for which this bound ... More

Unfolding homoclinic connections formed by corner intersections in piecewise-smooth mapsMar 16 2016The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its stable manifold ... More

Parametric representation of univalent functions with boundary regular fixed pointsMar 13 2016Mar 30 2016Given a set $\mathfrak S$ of conformal maps of the unit disk $\mathbb D$ into itself that is closed under composition, we address the question whether $\mathfrak S$ can be represented as the reachable set of a Loewner - Kufarev - type ODE $\mathrm{d}w_t/\mathrm{d}t=G_t\circ ... More

Finite orbits for nilpotent actions on the torusMar 13 2016A homeomorphism of the $2$-torus with Lefschetz number different from zero has a fixed point. We give a version of this result for nilpotent groups of diffeomorphisms. We prove that a nilpotent group of $2$-torus diffeomorphims has finite orbits when ... More

New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariantMar 05 2016We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. ... More

Minimal dilatation in Penner's constructionFeb 24 2016For all orientable closed surfaces, we determine the minimal dilatation among mapping classes arising from Penner's construction. We also discuss generalisations to surfaces with punctures.

A note on covers of fibred hyperbolic manifoldsFeb 18 2016For each surface $S$ of genus $g>2$ we construct pairs of conjugate pseudo-Anosov maps, $\varphi_1$ and $\varphi_2$, and two non-equivalent covers $p_i: \tilde S \longrightarrow S$, $i=1,2$, so that the lift of $\varphi_1$ to $\tilde S$ with respect to ... More

Generalized beta-transformations and the entropy of unimodal mapsFeb 10 2016Feb 17 2016Generalized beta-transformations are the class of piecewise continuous interval maps given by taking the beta-transformation $x \mapsto \beta x ~\pmod 1$, where $\beta>1$, and replacing some of the branches with branches of constant negative slope. If ... More

Some properties of Hamiltonian homeomorphisms on closed aspherical surfacesFeb 07 2016Jun 13 2016On closed symplectically aspherical manifolds, Schwarz proved a classical result that the action function of a nontrivial Hamiltonian diffeomorphism is not constant by using Floer homology. In this article, we generalize Schwarz's theorem to the $C^0$-case ... More

Some properties of Hamiltonian homeomorphisms on closed aspherical surfacesFeb 07 2016Oct 21 2016On closed symplectically aspherical manifolds, Schwarz proved a classical result that the action function of a nontrivial Hamiltonian diffeomorphism is not constant by using Floer homology. In this article, we generalize Schwarz's theorem to the $C^0$-case ... More

Symbolic dynamics for Lozi mapsJan 08 2016In this paper we study the family of the Lozi maps $L_{a,b} : {\mathbb R}^2 \to {\mathbb R}^2$, $L_{a,b} = (1 + y - a|x|, bx)$, and their strange attractors $\Lambda_{a,b}$. We introduce the set of kneading sequences for the Lozi map and prove that it ... More

A $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfacesDec 20 2015Sep 14 2016We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of spectral invariants ... More

Equivariant A-infinity algebras for nonorientable LagrangiansDec 14 2015Jan 28 2016We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted $A_\infty$ algebras ... More

Jordan groups, conic bundles and abelian varietiesDec 06 2015Jul 04 2016A group $G$ is called Jordan if there is a positive integer $J=J_G$ such that every finite subgroup $\mathcal{B}$ of $G$ contains a commutative subgroup $\mathcal{A}\subset \mathcal{B}$ such that $\mathcal{A}$ is normal in $\mathcal{B}$ and the index ... More

Lattice Surfaces and smallest trianglesDec 02 2015Mar 06 2016We calculate the area of the smallest triangle and the area of the smallest virtual triangle for many known lattice surfaces. We show that our list of the lattice surfaces for which the area of the smallest virtual triangle greater than .05 is complete. ... More

Slow north-south dynamics on $\mathcal{PML}$Dec 02 2015May 11 2016We consider the action of a pseudo-Anosov mapping class on $\mathcal{PML}(S)$. This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples ... More

A refinement of a theorem by FranksNov 21 2015Jan 18 2016In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

Universality in halting time and its applications in optimizationNov 19 2015Jan 12 2016The authors present empirical universal distributions for the halting time (measured by the number of iterations to reach a given accuracy) of optimization algorithms applied to two random systems: spin glasses and deep learning. Given an algorithm, which ... More

Entropy in the cusp and phase transitions for geodesic flowsNov 12 2015Jan 27 2016In this paper we study the geodesic flow for a particular class of Riemannian non-compact manifolds with variable pinched negative sectional curvature. For a sequence of invariant measures we are able to prove results relating the loss of mass and bounds ... More

Topological extension of Calabi homomorphism and non-simpleness of the area-preserving homeomorphism group of two-discOct 25 2015Nov 05 2015The paper contains a silly mistake in the usage of the equation (5.4) in the formula (6.5). Due to this mistake, the effect of the transfer map $phi$ is nullified. I am deeply sorry for not being very careful in my submission and making this mistake.

On a generalization of the Cartwright-Littlewood fixed point theorem for planar homeomorphismsOct 22 2015We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose $h : \mathbb{R}^2 \to\mathbb{R}^2$ is an orientation preserving planar homeomorphism, and let $C$ be a continuum such that $h^{-1}(C)\cup C$ is acyclic. ... More

On the Integral Representation of Binary Quadratic Forms and the Artin ConditionOct 16 2015For diophantine equations of the form ax^2+bxy+cy^2+g=0 over Z whose coefficients satisfy some hypotheses, we show that the Artin condition is the only obstruction to the local-global principle for integral solutions of the equation. Some concrete examples ... More

On the Integral Representation of Binary Quadratic Forms and the Artin ConditionOct 16 2015Dec 06 2016For diophantine equations of the form ax^2+bxy+cy^2+g=0 over Z whose coefficients satisfy some assumptions, we show that a condition with respect to Artin reciprocity map, which we call the Artin condition, is the only obstruction to the local-global ... More

Auslander-Reiten quiver and representation theories related to KLR-type Schur-Weyl dualitySep 16 2015Apr 25 2016We introduce new notions on the sequences of positive roots by using Auslander-Reiten quivers. Then we can prove that the new notions provide interesting information on the representation theories of KLR-algebras, quantum groups and quantum affine algebras ... More

Combinatorial Auslander-Reiten quivers and reduced expressionsSep 16 2015In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers. Combinatorial AR quivers can be understood as a generalization of AR quivers and each combinatorial AR quiver realizes a convex partial order on a set of positive roots ... More

Steady-State Solutions in an Algebra of Generalized FunctionsSep 13 2015Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of generalized ... More

Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometryAug 22 2015In recent years it has been noted that a number of combinatorial structures such as real and complex hyperplane arrangements, interval greedoids, matroids and oriented matroids have the structure of a finite monoid called a left regular band. Random walks ... More

Linear response for intermittent mapsAug 11 2015Feb 16 2016We consider the one parameter family $\alpha \mapsto T_\alpha$ ($\alpha \in [0,1)$) of Pomeau-Manneville type interval maps $T_\alpha(x)=x(1+2^\alpha x^\alpha)$ for $x \in [0,1/2)$ and $T_\alpha(x)=2x-1$ for $x \in [1/2, 1]$, with the associated absolutely ... More

Central limit theorem for generalized Weierstrass functionsAug 09 2015Jul 13 2016Let $f$ be a $C^{2+\epsilon}$ expanding map of the circle and $v$ be a $C^{1+\epsilon}$ real function of the circle. Consider the twisted cohomological equation $v(x) = \alpha (f(x)) - Df(x) \alpha (x)$ which has a unique bounded solution $\alpha$. We ... More

On the Dynamics of a Third Order Newton's Approximation MethodJul 27 2015Mar 22 2016We show that the third order approximation function $M_f$, proposed by S. Amat, S. Busquier, S. Plaza, in \textit{J. Math. Anal. Appl.}, 366(2010), 24--32, for functions $f$ twice continuously differentiable and such that both $f$ and its derivative do ... More

Fully essential dynamics for area-preserving surface homeomorphismsJul 16 2015Jun 04 2016We study the interplay between the dynamics of area-preserving surface homeomorphisms homotopic to the identity and the topology of the surface. We define fully essential dynamics and generalize the results previously obtained on strictly toral dynamics ... More

Fully essential dynamics for area-preserving surface homeomorphismsJul 16 2015Nov 17 2016We study the interplay between the dynamics of area-preserving surface homeomorphisms homotopic to the identity and the topology of the surface. We define fully essential dynamics and generalize the results previously obtained on strictly toral dynamics ... More

Sobolev regularity of the Beurling transform on planar domainsJul 15 2015May 11 2016Consider a Lipschitz domain $\Omega$ and the Beurling transform of its characteristic function $\mathcal{B} \chi_\Omega(z)= - {\rm p.v.}\frac1{\pi z^2}*\chi_\Omega (z) $. It is shown that if the outward unit normal vector $N$ of the boundary of the domain ... More

Sobolev regularity of quasiconformal mappings on domainsJul 15 2015Sep 07 2015Consider a Lipschitz domain $\Omega$ and a measurable function $\mu$ supported in $\overline\Omega$ with $\left\|{\mu}\right\|_{L^\infty}<1$. Then the derivatives of a quasiconformal solution of the Beltrami equation $\overline{\partial} f =\mu \partial ... More

Dualities and derived equivalences for category OJun 29 2015Jun 18 2016We determine the Ringel duals for all blocks in the parabolic versions of the BGG category O associated to a reductive finite dimensional Lie algebra. In particular we find that, contrary to the original category O and the specific previously known cases ... More

Möbius disjointness for homogeneous dynamicsJun 25 2015Oct 16 2016We prove Sarnak's M\"obius disjointness conjecture for all unipotent translations on homogeneous spaces of real connected Lie groups. Namely, we show that if $G$ is any such group, $\Gamma\subset G$ a lattice, and $u\in G$ an Ad-unipotent element, then ... More

Weyl variations and local sufficiency of linear observers in the mean square optimal coherent quantum filtering problemJun 25 2015This paper is concerned with the coherent quantum filtering (CQF) problem, where a quantum observer is cascaded in a measurement-free fashion with a linear quantum plant so as to minimize a mean square error of estimating the plant variables of interest. ... More

Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamicsJun 24 2015We consider semigroup actions on the unit interval generated by strictly increasing $C^r$-maps. We assume that one of the generators has a pair of fixed points, one attracting and one repelling, and a heteroclinic orbit that connects the repeller and ... More

Conformal models and fingerprints of pseudo-lemniscatesJun 16 2015May 25 2016We prove that every function that is meromorphic on the closure of an analytic Jordan domain and sufficiently well-behaved on the boundary is conformally equivalent to a rational map whose degree is smallest possible. We also show that the minimality ... More

A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum controlJun 15 2015Aug 07 2015This paper is concerned with variational methods for nonlinear open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. The latter are driven by quantum Wiener processes of the external boson ... More

Braid Equivalence in the Hénon Family IJun 15 2015We give two general constructions of braid equivalences which exist between certain deformations of the 2-branched Horsehoe map. We then give numerical evidence suggesting that these constructions of braid equivalences are always realised in the H\'enon ... More

Exponential Decay of Correlations for Finite Horizon Sinai Billiard FlowsJun 09 2015We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding ... More

On Coxeter mapping classes and fibered alternating linksJun 05 2015Feb 21 2016Alternating-sign Hopf plumbing along a tree yields fibered alternating links whose homological monodromy is, up to a sign, conjugate to some alternating-sign Coxeter transformation. Exploiting this tie, we obtain results about the location of zeros of ... More

The Ext algebra and a new generalisation of D-Koszul algebrasJun 05 2015Oct 28 2015We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in degrees 0, ... More

Poincaré theory for decomposable cofrontiersJun 03 2015We extend Poincar\'e's theory of orientation-preserving homeomorphisms from the circle to circloids with decomposable boundary. As special cases, this includes both decomposable cofrontiers and decomposable cobasin boundaries. More precisely, we show ... More

Poincaré theory for decomposable cofrontiersJun 03 2015Nov 17 2016We extend Poincar\'e's theory of orientation-preserving homeomorphisms from the circle to circloids with decomposable boundary. As special cases, this includes both decomposable cofrontiers and decomposable cobasin boundaries. More precisely, we show ... More

Quantitative Recurrence for Generic HomeomorphismsMay 11 2015In this article we study quantitative recurrence for generic home- omorphisms on euclidian spaces and compact manifolds. As an application we show that the decay of correlations of generic homeomorphisms is slow.

Bijective Deformations in $\mathbb{R}^n$ via Integral Curve CoordinatesMay 01 2015We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum, in the domain, ... More

Forcing theory for transverse trajectories of surface homeomorphismsMar 31 2015Nov 20 2015This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and Brouwer theory. The main development is a novel theory of orbit forcing using maximal isotopies and transverse foliations. This allows us ... More

Ring homeomorphisms and prime endsMar 30 2015We show that every homeomorphic $W^{1,1}_{\rm loc}$ solution $f$ of a Beltrami equation $\overline{\partial}f=\mu\,\partial f$ in a domain $D\subseteq\Bbb C$ is the so--called ring $Q-$homeomorphism with $Q(z)=K^T_{\mu}(z, z_0)$ where $K^T_{\mu}(z, z_0)$ ... More

From self-similar groups to self-similar sets and spectraMar 24 2015The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.

Effective equidistribution and property tauMar 19 2015We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters. We explain how this implies certain equidistribution theorems ... More

The Dirichlet problem and prime endsMar 14 2015Mar 29 2015It is developed the theory of the boundary behavior of homeomorphic solutions of the Beltrami equations ${\bar{\partial}}f=\mu\,{\partial}f$ of the Sobolev class $W^{1,1}_{\rm loc}$ with respect to prime ends of domains. On this basis, under certain conditions ... More

Central limit theorem for the modulus of continuity of averages of observables on transversal families of piecewise expanding unimodal mapsMar 04 2015Apr 22 2016We prove that the Newton quotient of the average R(t) of a lipschitzian function (with non vanishing variation) with respect to the SRB measure on a transversal family f_t of piecewise expanding unimodal maps, after an appropriated normalization, converges ... More

On the construction of integrated vertex in the pure spinor formalism in curved backgroundMar 03 2015Jun 24 2015We have previously described a way of describing the relation between unintegrated and integrated vertex operators in AdS5xS5 which uses the interpretation of the BRST cohomology as a Lie algebra cohomology and integrability properties of the AdS background. ... More

The spectrum of Volterra operators on weighted spaces of entire functionsFeb 27 2015We investigate the spectrum of the Volterra operator $V_g$ with symbol an entire function $g$, when it acts on weighted Banach spaces $H_v^{\infty}(\mathbb{C})$ of entire functions with sup-norms and when it acts on H\"ormander algebras $A_p$ or $A^0_p$. ... More

Decompositions of rational functions over real and complex numbers and a question about invariant curvesFeb 25 2015We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.

The strong "zero-two" law for positive contractions of Banach-Kantorovich L_p-latticesFeb 25 2015In the present paper we study majorizable operators acting on Banach-Kantorovich $L_p$-lattices, constructed by a measure $m$ with values in the ring of all measurable functions. Then using methods of measurable bundles of Banach-Kantorovich lattices, ... More

On boundary behavior of mappings with finite distortion in the planeFeb 05 2015Feb 08 2015In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions on the function ... More

Birkhoff spectrum for Hénon-like maps at the first bifurcationJan 31 2015We effect a multifractal analysis for a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We decompose the set of non wandering ... More

Most linear flows on $\mathbb{R}^d$ are BenfordJan 21 2015A necessary and sufficient condition ("exponential nonresonance") is established for every signal obtained from a linear flow on $\mathbb{R}^d$ by means of a linear observable to either vanish identically or else exhibit a strong form of Benford's Law ... More

A survey of some arithmetic applications of ergodic theory in negative curvatureJan 09 2015This paper is a survey of some arithmetic applications of techniques in the geometry and ergodic theory of negatively curved Riemannian manifolds, focusing on the joint works of the authors. We describe Diophantine approximation results of real numbers ... More

Equilibrium measures at temperature zero for Hénon-like maps at the first bifurcationDec 27 2014We develop a thermodynamic formalism for a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. For any $t\in\mathbb R$ we prove the ... More

Dynamics of the monodromies of the fibrations on the magic 3-manifoldDec 24 2014We study the magic manifold $N$ which is a hyperbolic and fibered $3$-manifold. We give an explicit construction of a fiber $F_a$ and its monodromy $:F_a \rightarrow F_a$ of the fibration associated to each fibered class $a$ of $N$. Let $\delta_g$ (resp. ... More

On the diagonal subalgebra of an Ext algebraDec 16 2014Let $R$ be a Koszul algebra over a field $k$ and $M$ be a linear $R$-module. We study a graded subalgebra $\Delta_M$ of the Ext-algebra $\operatorname{Ext}_R^*(M,M)$ called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ... More