Deviation of ergodic averages for rational polygonal billiards

DOI10.1215/00127094-2008-037zbMath1153.37001arXivmath/0701658OpenAlexW2031404185MaRDI QIDQ939646

Giovanni Forni, Jayadev S. Athreya

Publication date: 28 August 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701658

zbMATH Keywords

rational polygonal billiardsdeviation of ergodic averages

Mathematics Subject Classification ID

Related Items (12)

Quantitative shrinking target properties for rotations and interval exchanges ⋮ Invariant and stationary measures for the \(\mathrm{SL}(2,\mathbb{R})\) action on moduli space ⋮ Quantitative mixing for locally Hamiltonian flows with saddle loops on compact surfaces ⋮ Effective mapping class group dynamics. I: Counting lattice points in Teichmüller space ⋮ Quantitative weak mixing for interval exchange transformations ⋮ Teichmüller dynamics and unique ergodicity via currents and Hodge theory ⋮ Counting closed geodesics in strata ⋮ Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension ⋮ The WYSIWYG compactification ⋮ Twisted translation flows and effective weak mixing ⋮ Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards ⋮ Zero-one law for the rates of convergence in the Birkhoff ergodic theorem with continuous time

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Horocycle flow on geometrically finite surfaces
• Ergodicity of billiard flows and quadratic differentials
• The Teichmüller geodesic flow
• Gauss measures for transformations on the space of interval exchange maps
• Interval exchange transformations and 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
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Invariant distributions and time averages for horocycle flows
• Affine mappings of translation surfaces: Geometry and arithmetic
• Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
• Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
• Euler characteristics of Teichmüller curves in genus two
• Quantitative recurrence and large deviations for Teichmüller geodesic flow
• Asymptotic formulas on flat surfaces
• Billiards on almost integrable polyhedral surfaces
• Ergodicity of billiards in polygons: explicit examples
• Ergodicity of billiards in polygons
• Deviation for interval exchange transformations
• Equidistribution of nilflows and applications to theta sums

This page was built for publication: Deviation of ergodic averages for rational polygonal billiards