DIMENSIONAL CHARACTERISTICS OF THE NONWANDERING SETS OF OPEN BILLIARDS

DOI10.1017/S0004972715000817zbMath1357.37045MaRDI QIDQ3458392

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Publication date: 18 December 2015

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

zbMATH Keywords

dynamical systemsbilliardsHausdorff dimensionnonwandering set

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Cites Work

• Differentiability and analyticity of topological entropy for Anosov and geodesic flows
• Decay of solutions of the wave equation in the exterior of several convex bodies
• A lower bound for the smallest singular value of a matrix
• Differentiation of SRB states
• An estimate from above of the number of periodic orbits for semi- dispersed billiards
• Estimates of Hausdorff Dimension for Non-wandering Sets of Higher Dimensional Open Billiards
• Non-integrability of open billiard flows and Dolgopyat-type estimates
• Estimates of Hausdorff Dimension for the Non-Wandering Set of an Open Planar Billiard
• Dimension estimates in nonconformal hyperbolic dynamics*
• A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems
• The dimensions of a non-conformal repeller and an average conformal repeller

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