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Derived length of zero entropy groups acting on projective varieties in arbitrary characteristic -- A remark to a paper of Dinh-Oguiso-ZhangSep 18 2019Let $X$ be a projective variety of dimension $n\ge1$ over an algebraically closed field of arbitrary characteristic. We prove a Fujiki-Lieberman type theorem on the structure of the automorphism group of $X$. Let $G$ be a group of zero entropy automorphisms ... More
Characterization of toric systems via transport costsSep 15 2019We characterize completely integrable Hamiltonian systems inducing an effective Hamiltonian torus action as systems with zero transport costs w.r.t. the time-$T$ map where $T \in {\mathbb R}^n$ is the period of the acting $n$-torus.
Optimal robustness of passive discrete time systemsSep 15 2019We construct optimally robust realizations of a given rational transfer function that represents a passive discrete-time system. We link it to the solution set of linear matrix inequalities defining passive transfer functions. We also consider the problem ... More
The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locationsSep 15 2019In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of this process ... More
Galois orbits of torsion points near atoral setsSep 13 2019We prove that the Galois equidistribution of torsion points of the algebraic torus $\mathbb{G}_{m}^d$ extends to the singular test functions of the form $\log{|P|}$, where $P$ is a Laurent polynomial having algebraic coefficients that vanishes on the ... More
Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Hofstadter's butterfly, determinants, and loop soup entropySep 12 2019The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by complex-valued weights. When properly interpreted, these complex weights ... More
Probabilistic potential theory and induction of dynamical systemsSep 12 2019In this article, we outline a version of a balayage formula in probabilistic potential theory adapted to measure-preserving dynamical systems. This balayage identity generalizes the property that induced maps preserve the restriction of the original invariant ... More
Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov processSep 11 2019We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly selected continuous ... More
Conjugate points for systems of second-order ordinary differential equationsSep 11 2019We recall the notion of Jacobi fields, as it was extended to systems of second-order ordinary differential equations. Two points along a base integral curve are conjugate if there exists a non-trivial Jacobi field along that curve that vanishes on both ... More
$P$-adic monomial equations and their perturbationSep 10 2019In this paper, we describe the set of all solutions of monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, as an application of the result, we study several perturbations of the considered equation over $p$-adic field.
Chaotic behavior of the $p$-adic Potts-Bethe mapping IISep 10 2019In our previous investigations, we have developed the renormalization group method to $p$-adic $q$-state Potts model on the Cayley tree of order $k$. This method is closely related to the examination of dynamical behavior of the $p$-adic Potts-Bethe mapping ... More
Non-gaussian waves in Seba's billiardSep 08 2019The Seba billiard, a rectangular torus with a point scatterer, is a popular model to study the transition between integrability and chaos in quantum systems. Whereas such billiards are classically essentially integrable, they may display features such ... More
Horseshoes for singly thermostated hamiltoniansSep 06 2019This note studies 1 and 2 degree of freedom hamiltonian systems that are thermostated by a single-variable thermostat. Under certain conditions on the hamiltonian and thermostat, the existence of a horseshoe in the flow of the thermostated system is proven. ... More
Global effect of non-conservative perturbations on homoclinic orbitsSep 04 2019We study the effect of time-dependent, non-conservative perturbations on the dynamics along homoclinic orbits to a normally hyperbolic invariant manifold. We assume that the unperturbed system is Hamiltonian, and the normally hyperbolic invariant manifold ... More
Complex dynamics in generalizations of the Chaplygin sleighSep 03 2019The article considers Chaplygin sleigh on a plane in potential well, assuming that an external potential force is supplied at the mass center. Two particular cases are studied in some detail, namely, a one-dimensional potential valley and a potential ... More
Invariant measures for stochastic damped 2D Euler equationsSep 01 2019We study a two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$. In this paper, ... More
Hamiltonian Dynamics of Semiclassical Gaussian Wave Packets in Electromagnetic PotentialsAug 29 2019We extend our previous work on symplectic semiclassical Gaussian wave packet dynamics to incorporate electromagnetic interactions by including a vector potential. The main advantage of our formulation is that the equations of motion derived are naturally ... More
Spectral properties of graphs associated to the Basilica groupAug 28 2019We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the basilica group, the iterated monodromy group of the quadratic polynomial $z^2-1$. This group is an important example in the class of self-similar ... More
Waist theorems for Tonelli systems in higher dimensionsAug 27 2019We study the periodic orbits problem on energy levels of Tonelli Lagrangian systems over configuration spaces of arbitrary dimension. We show that, when the fundamental group is finite and the Lagrangian has no stationary orbit at the Ma\~n\'e critical ... More
Divisors on surfaces isogenous to a product of mixed type with $p_g=0$Aug 25 2019In this paper, we study effective, nef and semiample cones of surfaces isogenous to a product of mixed type with $p_g=0$. In particular, we prove that all reducible fake quadrics are Mori dream surfaces.
The Dirichlet problem for elliptic operators having a BMO anti-symmetric partAug 22 2019The present paper establishes the first result on the absolute continuity of elliptic measure with respect to the Lebesgue measure for a divergence form elliptic operator with non-smooth coefficients that have a BMO anti-symmetric part. In particular, ... More
Recovery of the Derivative of the Conductivity at the BoundaryAug 22 2019We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness of the conductivity in the bulk ... More
Stationary characters on lattices of semisimple Lie groupsAug 21 2019We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation theory, operator ... More
Irrationality and monodromy for cubic threefoldsAug 19 2019We show the cohomological monodromy for the universal family of smooth cubic threefolds does not factor through the genus five mapping class group. This gives a geometric group theory perspective on the well-known irrationality of cubic threefolds.
Irrationality and monodromy for cubic threefoldsAug 19 2019Aug 21 2019We show the cohomological monodromy for the universal family of smooth cubic threefolds does not factor through the genus five mapping class group. This gives a geometric group theory perspective on the well-known irrationality of cubic threefolds.
Irrationality and monodromy for cubic threefoldsAug 19 2019Sep 15 2019We show the cohomological monodromy for the universal family of smooth cubic threefolds does not factor through the genus five mapping class group. This gives a geometric group theory perspective on the well-known irrationality of cubic threefolds.
Dolbeault cohomology of complex manifolds with torus actionAug 18 2019Sep 16 2019We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality, complex manifolds ... More
Optimal scheduling of critically loaded multiclass GI/M/n+M queues in an alternating renewal environmentAug 17 2019In this paper, we study optimal control problems for multiclass GI/M/n+M queues in an alternating renewal (up-down) random environment in the Halfin-Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes ... More
On the anisotropic stable JCIR processAug 15 2019We investigate the anisotropic stable JCIR process which is a multi-dimensional extension of the stable JCIR process but also a multi-dimensional analogue of the classical JCIR process. We prove that the heat kernel of the anisotropic stable JCIR process ... More
Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic ForcingAug 13 2019We survey some recent developments in the analysis of the long-time behavior of stochastic solutions of nonlinear conservation laws driven by stochastic forcing. Moreover, we establish the existence and uniqueness of invariant measures for anisotropic ... More
Spectral and Dynamic Consequences of Network SpecializationAug 12 2019One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the function(s) they ... More
The Bilinear Strategy for Calderón's ProblemAug 12 2019Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the conductivity is indeed uniquely determined ... More
Fixed-Time Stable Proximal Dynamical System for Solving Mixed Variational Inequality ProblemsAug 09 2019Aug 12 2019In this paper, the fixed-time stability of a novel proximal dynamical system is investigated for solving mixed variational inequality problems. Under the assumptions of strong monotonicity and Lipschitz continuity, it is shown that the solution of the ... More
Geometric control theory of vertical rolling disc using symmetriesAug 09 2019We use the methods of geometric control theory to study extremal trajectories of vertical rolling disk. We focus on the role of symmetries of the underlying geometric structures. We demonstrate the computations in the CAS Maple package DifferentialGeometry. ... More
The regularity problem for uniformly elliptic operators in weighted spacesAug 09 2019This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the boundary data belongs to Lebesgue spaces with weights in the Muckenhoupt classes. ... More
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant caseAug 08 2019This is the second part of a series of two papers where we study the connection between the $A_\infty$ property of the elliptic measures associated with second order divergence form elliptic operators on some given domain and the uniform rectifiability ... More
Projectively equivalent Finsler metrics on surfaces of negative Euler characteristicAug 07 2019Aug 08 2019We proof that on a surface of negative Euler characteristic, two real-analytic Finsler metrics have the same unparametrized oriented geodesics, if and only if they differ by a scaling constant and addition of a closed 1-form.
Escaping orbits are also rare in the almost periodic Fermi-Ulam ping-pongAug 07 2019We study the one-dimensional Fermi-Ulam ping-pong problem with a Bohr almost periodic forcing function and show that the set of initial condition leading to escaping orbits typically has Lebesgue measure zero.
Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimatesAug 06 2019We generalize to the setting of 1-sided chord-arc domains, that is, to domains satisfying the interior Corkscrew and Harnack Chain conditions (these are respectively scale-invariant/quantitative versions of the openness and path-connectedness) and which ... More
$L^p$ theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric partAug 02 2019We consider the operator $L=-{\rm div}(A\nabla)$, where the $n\times n$ matrix $A$ is real-valued, elliptic, with the symmetric part of $A$ in $L^\infty(\mathbb{R}^n)$, and the anti-symmetric part of $A$ only belongs to the space $BMO(\mathbb{R}^n)$, ... More
Combinatorics of periodic ellipsoidal billiardsAug 02 2019We study combinatorics of billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d-dimensional Euclidean and pseudo-Euclidean spaces. Such partitions uniquely codify the sets of caustics, up to ... More
User guide on Hopf bifurcation and time periodic orbits with pde2pathAug 02 2019We explain the setup for using the pde2path libraries for Hopf bifurcation and continuation of branches of periodic orbits and give implementation details of the associated demo directories. See [Uecker, Comm. in Comp. Phys., 2019] for a description of ... More
Pattern formation with pde2path -- a tutorialAug 02 2019We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review general concepts ... More
Linear Stability of Elliptic Relative Equilibria of Restricted Four-body ProblemJul 31 2019In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincar\'e map is decomposed to the essential part, ... More
Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal massesJul 31 2019In this paper, we consider the elliptic relative equilibria of four-body problem with two infinitesimal masses. The most interesting case is when the two small masses tend to the same Lagrangian point $L_4$ (or $L_5$). In \cite{Xia}, Z. Xia showed that ... More
Wave propagation for reaction-diffusion equations on infinite random treesJul 30 2019The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provided that the reaction rate is large enough. The wavefront travels at a speed ... More
Wave propagation for reaction-diffusion equations on infinite random treesJul 30 2019Aug 14 2019The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provided that the reaction rate is large enough. The wavefront travels at a speed ... More
Closed form solutions of Lucas Uzawa model with externalities via partial Hamiltonian approach. Some ClarificationsJul 29 2019The main aim of this paper is to give some clarifications to the recent paper published in Computational and Applied Mathematics by Naz and Chaudhry.
Stochastic Tverberg theorems and their applications in multi-class logistic regression, data separability, and centerpoints of dataJul 23 2019We present new stochastic geometry theorems that give bounds on the probability that $m$ random data classes all contain a point in common in their convex hulls. We apply these stochastic separation theorems to obtain bounds on the probability of existence ... More
Heteroclinic solutions for a generalized Frenkel-Kontorova model by minimization methods of Rabinowitz and StredulinskyJul 19 2019We study heteroclinic solutions of a generalized Frenkel-Kontorova model. Using the methods of Rabinowitz and Stredulinsky, we prove that if the rotation vector of the configuration is rational and if there is an adjacent pair of periodic configurations, ... More
Collective Heavy Top DynamicsJul 18 2019We construct a Poisson map $\mathbf{M}\colon T^{*}\mathbb{C}^{2} \to \mathfrak{se}(3)^{*}$ with respect to the canonical Poisson bracket on $T^{*}\mathbb{C}^{2} \cong T^{*}\mathbb{R}^{4}$ and the $(-)$-Lie--Poisson bracket on the dual $\mathfrak{se}(3)^{*}$ ... More
New integrable two-centre problem on sphere in Dirac magnetic fieldJul 14 2019We present a new integrable version of the two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole. The new system can be written on the dual space of Lie algebra $e(3)$ and is integrable both in classical and quantum ... More
Attractors of Hamilton nonlinear partial differential equationsJul 13 2019We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamics ... More
Lectures on Quantum Mechanics for mathematiciansJul 12 2019The first main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary orbits, ... More
Lectures on Quantum Mechanics for mathematiciansJul 12 2019Jul 15 2019The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary orbits, wave-particle ... More
On different expressions for invariants of hyperelliptic curves of genus 3Jul 12 2019In this paper we give a passage formula between different invariants of genus 3 hyperelliptic curves: in particular between Tsuyumine and Shioda invariants. This is needed to get modular expressions for Shioda invariants, that is, for example, useful ... More
Local Limit Theorems for the Random Conductance Model and Applications to the Ginzburg-Landau $\nabla\varphi$ Interface ModelJul 11 2019We study a continuous-time random walk on $\mathbb{Z}^d$ in an environment of random conductances taking values in $(0,\infty)$. For a static environment, we extend the quenched local limit theorem to the case of a general speed measure, given suitable ... More
Discontinuous Galerkin discretization for two-equation turbulence closure modelJul 10 2019Accurate representation of vertical turbulence is crucial for numerical ocean modelling, both in global and coastal applications. The state-of-the-art approach is to use two-equation turbulence closure models which introduces two dynamic equations to ... More
Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flowsJul 09 2019Jul 25 2019We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxwell and Kaluza--Klein, KK, theories formulated in Lagrange-Hamilton and general covariant variables. There are considered nonholonomic deformations of Grigory ... More
Revisiting Biorthogonal Polynomials. An $LU$ factorization discussionJul 09 2019The Gauss-Borel or $LU$ factorization of Gram matrices of bilinear forms is the pivotal element in the discussion of the theory of biorthogonal polynomials. The construction of biorthogonal families of polynomials and its second kind functions, of the ... More
Etalumis: Bringing Probabilistic Programming to Scientific Simulators at ScaleJul 08 2019Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting complex scientific ... More
Etalumis: Bringing Probabilistic Programming to Scientific Simulators at ScaleJul 08 2019Aug 27 2019Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting complex scientific ... More
New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetriesJul 05 2019Jul 22 2019We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying ... More
Mean-field analysis of multi-population dynamics with label switchingJul 05 2019The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given population. ... More
Mean-field analysis of multi-population dynamics with label switchingJul 05 2019Jul 11 2019The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given population. ... More
Harmonic measure and quantitative connectivity: geometric characterization of the $L^p$-solvability of the Dirichlet problemJul 04 2019It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak-$A_\infty$ property) of harmonic measure with respect to surface measure, on the boundary of an open set $ \Omega\subset \mathbb{R}^{n+1}$ with Ahlfors-David ... More
Non-regular g-measures and variable length memory chainsJul 04 2019It is well-known that there always exists at least one stationary measure compatible with a continuous g-function g. Here we prove that if the set of discontinuities of the g-function g has null measure under a candidate measure obtained by some asymptotic ... More
Covariant momentum map for non-Abelian topological BF field theoryJul 02 2019We analyze the inherent symmetries associated to the non-Abelian topological BF theory from the geometric and covariant perspectives of the Lagrangian and the multisymplectic formalisms. At the Lagrangian level, we classify the symmetries of the theory ... More
A transcendental dynamical degreeJul 01 2019We give an example of a dominant rational selfmap of the projective plane whose dynamical degree is a transcendental number.
Free abelian group actions on normal projective varieties: sub-maximal dynamical rank caseJun 29 2019Let $X$ be a normal projective variety of dimension $n$ and $G$ an abelian group of automorphisms such that all elements of $G\setminus \{\mathrm{id}\}$ are of positive entropy. Dinh and Sibony showed that $G$ is actually free abelian of rank $\le n - ... More
Bi-rational maps in four dimensions with two invariantsJun 28 2019In this paper we present a class of four-dimensional bi-rational maps with two invariants satisfying certain constraints on degrees. We discuss the integrability properties of these maps from the point of view of degree growth and Liouville integrability. ... More
A note on Lyapunov instability in Newtonian dynamicsJun 27 2019In the class of analytic potentials, we give a new sufficient condition for the Lyapunov instability of a local minimum of the potential. In contrast with similar analytical results concerning the first non zero jet of the potential, this new condition ... More
$T$-equivariant disc potential and SYZ mirror constructionJun 27 2019Sep 13 2019We develop a $G$-equivariant Lagrangian Floer theory by counting pearly trees in the Borel construction $L_G$. We apply the construction to smooth moment-map fibers of toric semi-Fano varieties and obtain the $T$-equivariant Landau-Ginzburg mirrors. We ... More
$T$-equivariant disc potential and SYZ mirror constructionJun 27 2019We develop a $G$-equivariant Lagrangian Floer theory by counting pearly trees in the Borel construction $L_G$. We apply the construction to smooth moment-map fibers of toric semi-Fano varieties and obtain the $T$-equivariant Landau-Ginzburg mirrors. We ... More
The Hamiltonian approach to the problem of derivation of production functions in economic growth theoryJun 26 2019We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we investigate some ... More
Levy-Khintchin Theorem for best simultaneous Diophantine approximationsJun 26 2019We extend two results about the ordinary continued fraction expansion to best simultaneous Diophantine approximations of vectors or matrices. The first is Levy-Khintchin Theorem about the almost sure growth rate of the denominators of the convergents. ... More
On Poisson structures arising from a Lie group actionJun 26 2019We investigate some infinite dimensional Lie algebras and their associated Poisson structures which arise from a Lie group action on a manifold. If $G$ is a Lie group, $\g$ its Lie algebra and $M$ is a manifold on which $G$ acts, then the set of smooth ... More
Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flowsJun 21 2019Jul 25 2019In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by stochastic differential ... More
Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchinJun 20 2019In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Levy noise with regime-switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein-Uhlenbeck process ... More
The existence of optimal control for continuous-time Markov decision processes in random environmentsJun 20 2019In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria. Under appropriate ... More
On chains and Rota-Baxter operators of evolution algebrasJun 19 2019The paper is devoted to study new classes of chains of evolution algebras and their time-depending dynamics. Moreover, we construct some Rote-Baxter operators of such algebras.
Chaos and integrability in SL(2,R)-geometryJun 19 2019The integrability of the geodesic flow on the three-folds $\mathcal M^3$ admitting $SL(2,\mathbb R)$-geometry in Thurston's sense is investigated. The main examples are the quotients $\mathcal M^3_\Gamma=\Gamma\backslash PSL(2,\mathbb R)$, where $\Gamma ... More
Homology, lower central series, and hyperplane arrangementsJun 12 2019We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain commuting diagrams. ... More
Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbationJun 11 2019When dynamical systems producing rhythmic behavior operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include heel-ground ... More
Gait modeling and optimization for the perturbed Stokes regimeJun 11 2019Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the "Stokesian" (viscous; ... More
Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion SystemsJun 08 2019We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. ... More
BRST-BFV and BRST-BV Lagrangians for Bosonic Fields with Continuous Spin on $R^{1,d-1}$Jun 06 2019Gauge-invariant Lagrangian descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST--BFV approach we propose. The resulting ... More
BRST-BFV and BRST-BV Lagrangians for Bosonic Fields with Continuous Spin on $R^{1,d-1}$Jun 06 2019Jul 16 2019Gauge-invariant Lagrangian descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST--BFV approach we propose. The resulting ... More
BRST-BFV and BRST-BV Lagrangians for Bosonic Fields with Continuous Spin on $R^{1,d-1}$Jun 06 2019Jun 10 2019Gauge-invariant Lagrangian descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST--BFV approach we propose. The resulting ... More
BRST-BFV and BRST-BV Lagrangians for Bosonic Fields with Continuous Spin on $R^{1,d-1}$Jun 06 2019Jul 24 2019Gauge-invariant Lagrangian descriptions for a free bosonic scalar field of continuous spin in a $d$-dimensional Minkowski space-time using a metric-like formulation are constructed on the basis of a constrained BRST--BFV approach we propose. The resulting ... More
Periodic solutions of symmetric Hamiltonian systemsJun 06 2019This paper is devoted to the study of periodic solutions of Hamiltonian system $\dot z(t)=J \nabla H(z(t))$, where $H$ is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a nearby of non-isolated critical points ... More
Periodic solutions of symmetric Hamiltonian systemsJun 06 2019Jun 10 2019This paper is devoted to the study of periodic solutions of Hamiltonian system $\dot z(t)=J \nabla H(z(t))$, where $H$ is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a nearby of non-isolated critical points ... More
Convergence of the solutions of the MFG discounted Hamilton-Jacobi equationJun 04 2019We consider the solution $\mathcal V_\delta$ of the discounted Hamilton-Jacobi equation in the Wasserstein space arising from potential MFG and we prove its full convergence to a corrector function $\chi_0$. We follow the structure of the proof of the ... More
On the divergence of Birkhoff Normal FormsJun 03 2019It is well known that a real analytic symplectic diffeomorphism of the two-dimensional annulus admitting a real analytic invariant curve with diophantine rotation number can be {\it formally} conjugated to its Birkhoff Normal Form, a formal power series ... More
Integrability of the $n$-dimensional axially symmetric Chaplygin sphereJun 01 2019Jun 08 2019We consider the $n$-dimensional Chaplygin sphere under the assumption that the mass distribution of the sphere is axisymmetric. We prove that for initial conditions whose angular momentum about the contact point is vertical, the dynamics is quasi-periodic. ... More
The axisymmetric Chaplygin sphereJun 01 2019We consider the $n$-dimensional Chaplygin sphere under the assumption that the mass distribution of the sphere is axisymmetric. We prove that for initial conditions whose angular momentum about the contact point is vertical, the dynamics is quasi-periodic. ... More
Integrability of the $n$-dimensional axially symmetric Chaplygin sphereJun 01 2019Aug 30 2019We consider the $n$-dimensional Chaplygin sphere under the assumption that the mass distribution of the sphere is axisymmetric. We prove that for initial conditions whose angular momentum about the contact point is vertical, the dynamics is quasi-periodic. ... More
Topological Shapes and their SignificanceMay 31 2019Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.
Dynamical and topological obstructions to extending group actionsMay 28 2019Aug 04 2019We study cohomological obstructions to extending group actions on the boundary $\partial M$ of a $3$-manifold to a $C^0$-action on $M$ when $\partial M$ is diffeomorphic to a torus or a sphere. In particular, we show that for a $3$-manifold $M$ with torus ... More
Dynamical and topological obstructions to extending group actionsMay 28 2019We study cohomological obstructions to extending group actions on the boundary $\partial M$ of a $3$-manifold to a $C^0$-action on $M$ when $\partial M$ is diffeomorphic to a torus or a sphere. In particular, we show that for a $3$-manifold $M$ with torus ... More