Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity

DOI10.1016/j.ansens.2003.05.001zbMath1106.37018OpenAlexW2070178103MaRDI QIDQ4470741

Thomas A. Schmidt, Eugene Gutkin, Pascal Hubert

Publication date: 15 June 2004

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_2003_4_36_6_847_0

Mathematics Subject Classification ID

Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Low-dimensional dynamical systems (37E99) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

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Cites Work

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• Quadratic differentials and foliations
• Ergodicity of billiard flows and quadratic differentials
• The Teichmüller geodesic flow
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• The billiard in a regular polygon
• Topological transitivity of billiards in polygons
• Billiards on rational-angled triangles
• Affine mappings of translation surfaces: Geometry and arithmetic
• Veech groups and polygonal coverings
• Continued fractions on the Veech surfaces
• Billiards in polygons: Survey of recent results.
• The geometry and arithmetic of translation surfaces with applications to polygonal billiards
• On the asymptotic quadratic growth rate of saddle connections and periodic orbits on marked flat tori.
• Concerning the transitive properties of geodesics on a rational polyhedron
• Asymptotic formulas on flat surfaces
• Billiards on almost integrable polyhedral surfaces
• On the geometry and dynamics of diffeomorphisms of surfaces
• Calculation of Fuchsian groups associated to billiards in a rational triangle
• Planar structures and billiards in rational polygons: the Veech alternative
• Invariants of translation surfaces
• On triangular billiards