Non-ergodic \(\mathbb{Z}\)-periodic billiards and infinite translation surfaces

DOI10.1007/s00222-013-0482-zzbMath1316.37006arXiv1109.4584OpenAlexW2069514721MaRDI QIDQ742830

Krzysztof Frączek, Corinna Ulcigrai

Publication date: 19 September 2014

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4584

zbMATH Keywords

ergodicitycocycletranslation surfacebilliard flow

Mathematics Subject Classification ID

Related Items (29)

Minimality of the Ehrenfest wind-tree model ⋮ Ergodicity of the Ehrenfest wind-tree model ⋮ Infinite type flat surface models of ergodic systems ⋮ Quantitative behavior of non-integrable systems. III ⋮ Ergodicity, mixing, Ratner's properties and disjointness for classical flows: on the research of Corinna Ulcigrai ⋮ 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 ⋮ Wild translation surfaces and infinite genus ⋮ Infinite ergodic index of the Ehrenfest wind-tree model ⋮ Ehrenfests' wind-tree model is dynamically richer than the Lorentz gas ⋮ Diffusion Rate of Windtree Models and Lyapunov Exponents ⋮ Ergodic properties of the ideal gas model for infinite billiards ⋮ Ergodic directions for billiards in a strip with periodically located obstacles ⋮ Invariance principle for the random wind-tree process ⋮ Every flat surface is Birkhoff and Oseledets generic in almost every direction ⋮ An infinite surface with the lattice property I: Veech groups and coding geodesics ⋮ Counting problem on wind-tree models ⋮ Residual generic ergodicity of periodic group extensions over translation surfaces ⋮ Periodicity and ergodicity in the trihexagonal tiling ⋮ Geometry of Refractions and Reflections Through a Biperiodic Medium ⋮ Exceptional ergodic directions in Eaton lenses ⋮ Genericity on curves and applications: pseudo-integrable billiards, Eaton lenses and gap distributions ⋮ Recurrence for the wind-tree model ⋮ The invariant measures of some infinite interval exchange maps ⋮ Rotational component spaces for infinite-type translation surfaces ⋮ Ergodicity of skew products over linearly recurrent IETs ⋮ Quantitative error term in the counting problem on Veech wind-tree models ⋮ Recurrent Sets for Ergodic Sums of an Integer Valued Function

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