On statistical properties of hyperbolic systems with singularities

DOI10.1007/s10955-009-9804-3zbMath1181.37052OpenAlexW2154428976MaRDI QIDQ1035829

Hong-Kun Zhang, Nikolai I. Chernov

Publication date: 4 November 2009

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-009-9804-3

zbMATH Keywords

invariant measuresSRB measuresexponential decay of correlationsstable manifoldmixing ratessmooth mapsBunimovich stadiumhyperbolic systems with singularitiesplanar billiardstwo-dimensional maps

Mathematics Subject Classification ID

Related Items (19)

Stable laws for chaotic billiards with cusps at flat points ⋮ Exponential mixing by orthogonal non-monotonic shears ⋮ Hyperbolic polygonal billiards with finitely many ergodic SRB measures ⋮ A piecewise smooth Fermi–Ulam pingpong with potential ⋮ Statistical properties of type D dispersing billiards ⋮ Exponential decay of random correlations for random Anosov systems mixing on fibers ⋮ Projective cones for sequential dispersing billiards ⋮ Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems ⋮ Exponential Fermi acceleration in a switching billiard ⋮ Electrical current in Sinai billiards under general small forces ⋮ Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps ⋮ Fluctuation of the entropy production for the Lorentz gas under small external forces ⋮ Non-stationary almost sure invariance principle for hyperbolic systems with singularities ⋮ SRB measures for polygonal billiards with contracting reflection laws ⋮ Current in periodic Lorentz gases with twists ⋮ Decay of correlations for billiards with flat points I: channel effects ⋮ Decay of correlations for billiards with flat points II: cusps effect ⋮ Convergence to a-stable Lévy motion for chaotic billiards with several cusps at flat points ⋮ Decay of correlations for unbounded observables

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