On the measure of maximal entropy for finite horizon Sinai Billiard maps

DOI10.1090/jams/939zbMath1444.37020arXiv1807.02330OpenAlexW3101934285WikidataQ126824543 ScholiaQ126824543MaRDI QIDQ5220195

Viviane Baladi, Mark F. Demers

Publication date: 11 March 2020

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.02330

zbMATH Keywords

topological entropytransfer operatormaximal entropy measureBowen-Margulis measureSinai billiard map

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Ergodicity, mixing, rates of mixing (37A25) Linear operators on function spaces (general) (47B38) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Topological entropy (37B40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (16)

State-to-state cosmology: a new view on the cosmological arrow of time and the past hypothesis ⋮ A convex analysis approach to entropy functions, variational principles and equilibrium states ⋮ Thermodynamic formalism for dispersing billiards ⋮ An upper bound on topological entropy of the Bunimovich stadium billiard map ⋮ Marked length spectral determination of analytic chaotic billiards with axial symmetries ⋮ Closed geodesics with prescribed intersection numbers ⋮ Topological entropy and pressure for finite-horizon Sinai billiards ⋮ Inducing schemes with finite weighted complexity ⋮ Rates of mixing for the measure of maximal entropy of dispersing billiard maps ⋮ Projective cones for sequential dispersing billiards ⋮ Equilibrium states for self‐products of flows and the mixing properties of rank 1 geodesic flows ⋮ Lyapunov exponents and nonadapted measures for dispersing billiards ⋮ Entropy rigidity for 3D conservative Anosov flows and dispersing billiards ⋮ Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps ⋮ Symbolic dynamics for non-uniformly hyperbolic systems ⋮ Entropy formula for systems with inducing schemes

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