On recurrence and ergodicity for geodesic flows on non-compact periodic polygonal surfaces

DOI10.1017/S0143385711001003zbMath1261.37018arXiv1008.0136OpenAlexW2963639928MaRDI QIDQ2908143

Jean-Pierre Conze, Eugene Gutkin

Publication date: 4 September 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0136

zbMATH Keywords

ergodicitycocyclesirrational rotationpolygonal billiardsconservativitydirectional billiard systemsLorenz gas

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (9)

On multiple ergodicity of affine cocycles over irrational rotations ⋮ Diffusive behavior of ergodic sums over rotations ⋮ On the CLT for rotations and BV functions ⋮ Periodic billiard orbits of self-similar Sierpiński carpets ⋮ Ergodic properties of infinite extensions of area-preserving flows ⋮ On the CLT for rotations and BV functions ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ The invariant measures of some infinite interval exchange maps ⋮ Non-ergodic \(\mathbb{Z}\)-periodic billiards and infinite translation surfaces

Cites Work

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• Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
• Cocycles over interval exchange transformations and multivalued Hamiltonian flows
• Ergodicity of cylinder flows arising from irregularities of distribution
• Ergodicity of billiard flows and quadratic differentials
• Billiard dynamics: a survey with the emphasis on open problems
• Affine mappings of translation surfaces: Geometry and arithmetic
• Billiards in polygons: Survey of recent results.
• The geometry and arithmetic of translation surfaces with applications to polygonal billiards
• Caustics for inner and outer billiards
• Recurrence in unipotent groups and ergodic nonabelian group extensions
• Growth rates for geometric complexities and counting functions in polygonal billiards
• Ergodic non-abelian smooth extensions of an irrational rotation
• Billiards on almost integrable polyhedral surfaces
• Recurrence of Co-Cycles and Random Walks
• On joint recurrence
• Ergodicity of billiards in polygons
• An Algorithm for Finding the Veech Group of an Origami

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