Ergodicity for infinite periodic translation surfaces

DOI10.1112/S0010437X12000887zbMath1348.37072arXiv1202.0156MaRDI QIDQ2852244

Pascal Hubert, Barak Weiss

Publication date: 8 October 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.0156

zbMATH Keywords

ergodicityinfiniteperiodictranslation surfaces

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Ergodicity, mixing, rates of mixing (37A25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Flows on surfaces (37E35)

Related Items (17)

The heights theorem for infinite Riemann surfaces ⋮ Minimality of the Ehrenfest wind-tree model ⋮ Ergodicity of the Ehrenfest wind-tree model ⋮ Quantitative behavior of non-integrable systems. III ⋮ Flat surfaces, Bratteli diagrams and unique ergodicity à la Masur ⋮ Immersions and translation structures I: The space of structures on the pointed disk ⋮ On ergodicity of foliations on \({\mathbb{Z}^d}\)-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses ⋮ Escape of mass and entropy for diagonal flows in real rank one situations ⋮ Ehrenfests' wind-tree model is dynamically richer than the Lorentz gas ⋮ Cocycles over interval exchange transformations and multivalued Hamiltonian flows ⋮ Ergodic directions for billiards in a strip with periodically located obstacles ⋮ An infinite surface with the lattice property I: Veech groups and coding geodesics ⋮ Periodicity and ergodicity in the trihexagonal tiling ⋮ Ergodic properties of infinite extensions of area-preserving flows ⋮ Exceptional ergodic directions in Eaton lenses ⋮ Non-ergodic \(\mathbb{Z}\)-periodic billiards and infinite translation surfaces ⋮ Indiscriminate covers of infinite translation surfaces are innocent, not devious

Cites Work

• Infinite translation surfaces with infinitely generated Veech groups
• Invariant measures and asymptotics for some skew products
• Generalized staircases: recurrence and symmetry
• Foliations with unbounded deviation on \(\mathbb T^2\)
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• Hausdorff dimension of the set of nonergodic foliations of a quadratic differential
• Diophantine approximation in Fuchsian groups

This page was built for publication: Ergodicity for infinite periodic translation surfaces