The geometry and arithmetic of translation surfaces with applications to polygonal billiards

DOI10.4310/MRL.1996.v3.n3.a8zbMath0865.30060OpenAlexW2324853665MaRDI QIDQ1815216

Eugene Gutkin, Christopher M. Judge

Publication date: 9 June 1997

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/mrl.1996.v3.n3.a8

zbMATH Keywords

translation surfacesVeech grouprational polygon

Mathematics Subject Classification ID

Teichmüller theory for Riemann surfaces (30F60) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Differentials on Riemann surfaces (30F30)

Related Items (16)

Infinitely generated Veech groups ⋮ On recurrence and ergodicity for geodesic flows on non-compact periodic polygonal surfaces ⋮ Prime arithmetic Teichmüller discs in \({\mathcal H}(2)\) ⋮ Generic absence of finite blocking for interior points of Birkhoff billiards ⋮ Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces ⋮ Periodic billiard orbits of self-similar Sierpiński carpets ⋮ Long hitting time for translation flows and L-shaped billiards ⋮ Invariants of translation surfaces ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ A higher moment formula for the Siegel-Veech transform over quotients by Hecke triangle groups ⋮ Veech surfaces and their periodic points ⋮ Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity ⋮ Affine mappings of translation surfaces: Geometry and arithmetic ⋮ Veech groups and polygonal coverings ⋮ Modular embeddings and rigidity for Fuchsian groups ⋮ Continued fractions on the Veech surfaces

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