On the ergodicity of flat surfaces of finite area

DOI10.1007/s00039-014-0269-4zbMath1300.37005arXiv1211.1313OpenAlexW2038851417MaRDI QIDQ2453454

Rodrigo Treviño

Publication date: 6 June 2014

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.1313

zbMATH Keywords

ergodicitysystolesaddle connectionflat surface

Mathematics Subject Classification ID

Related Items (16)

The heights theorem for infinite Riemann surfaces ⋮ Logarithmic laws and unique ergodicity ⋮ Infinite type flat surface models of ergodic systems ⋮ Flat surfaces, Bratteli diagrams and unique ergodicity à la Masur ⋮ Immersions and translation structures I: The space of structures on the pointed disk ⋮ Meromorphic \(L^2\) functions on flat surfaces ⋮ Wild translation surfaces and infinite genus ⋮ Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation ⋮ The complete family of Arnoux-Yoccoz surfaces ⋮ Teichmüller dynamics and unique ergodicity via currents and Hodge theory ⋮ Bill Veech's contributions to dynamical systems ⋮ The invariant measures of some infinite interval exchange maps ⋮ A smooth mixing flow on a surface with nondegenerate fixed points ⋮ Indiscriminate covers of infinite translation surfaces are innocent, not devious ⋮ Rotational component spaces for infinite-type translation surfaces ⋮ Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards

Cites Work

• Quadratic differentials and foliations
• Infinite translation surfaces with infinitely generated Veech groups
• Ergodicity of billiard flows and quadratic differentials
• The Teichmüller geodesic flow
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• Interval exchange transformations and measured foliations
• Hausdorff dimension of sets of nonergodic measured foliations
• Hausdorff dimension of the set of nonergodic foliations of a quadratic differential
• Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher genus
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• Ergodic infinite group extensions of geodesic flows on translation surfaces
• The invariant measures of some infinite interval exchange maps
• Weak mixing for interval exchange transformations and translation flows
• Boshernitzan's criterion for unique ergodicity of an interval exchange transformation
• An infinite surface with the lattice property I: Veech groups and coding geodesics
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