Veech groups without parabolic elements

DOI10.1215/S0012-7094-06-13326-4zbMath1101.30044arXivmath/0503047OpenAlexW2045215902WikidataQ56687669 ScholiaQ56687669MaRDI QIDQ2496932

Pascal Hubert, Erwan Lanneau

Publication date: 25 July 2006

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

Full work available at URL: https://arxiv.org/abs/math/0503047

zbMATH Keywords

translation surfaceVeech groupparabolic element

Mathematics Subject Classification ID

Klein surfaces (30F50) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items

Billiards and Teichmüller curves ⋮ New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant ⋮ Billiards, heights, and the arithmetic of non-arithmetic groups ⋮ Infinite type flat surface models of ergodic systems ⋮ Topological Veech dichotomy and tessellations of the hyperbolic plane ⋮ Translation surfaces and the curve graph in genus two ⋮ Infinitely many lattice surfaces with special pseudo-Anosov maps ⋮ The Deligne-Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3 ⋮ Computing periodic points on Veech surfaces ⋮ A construction of pseudo-Anosov homeomorphisms using positive twists ⋮ Completely periodic directions and orbit closures of many pseudo-Anosov Teichmüller discs in \(\mathrm{Q}(1,1,1,1)\). ⋮ Constructing lattice surfaces with prescribed Veech groups: an algorithm ⋮ The complete family of Arnoux-Yoccoz surfaces ⋮ Salem number stretch factors and totally real fields arising from Thurston's construction ⋮ Diophantine approximation on Veech surfaces ⋮ Hyperbolic lengths of some filling geodesics on Riemann surfaces with punctures ⋮ Fundamental domains and generators for lattice Veech groups ⋮ Persistence of wandering intervals in self-similar affine interval exchange transformations ⋮ Geometrical Models for Substitutions ⋮ Finiteness results for Teichmüller curves ⋮ Weak mixing directions in non-arithmetic Veech surfaces ⋮ ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS ⋮ Book Review: Twisted Teichmüller curves ⋮ Modular symbols for Teichmüller curves ⋮ The Arnoux-Yoccoz mapping classes via Penner's construction ⋮ Veech groups of flat surfaces with poles ⋮ Pseudo-Anosov mapping classes and their representations by products of two Dehn twists

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• A cutting and pasting of noncompact polygons with applications to Fuchsian groups
• Gauss measures for transformations on the space of interval exchange maps
• The billiard in a regular polygon
• Billiards on rational-angled triangles
• Affine mappings of translation surfaces: Geometry and arithmetic
• Infinitely generated Veech groups
• Teichmüller geodesics of infinite complexity.
• Prime arithmetic Teichmüller discs in \({\mathcal H}(2)\)
• On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number
• Teichmüller curves in genus two: Torsion divisors and ratios of sines
• Teichmüller curves in genus two: Discriminant and spin
• Variations of Hodge structures of a Teichmüller curve
• 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
• Billiards and Teichmüller curves on Hilbert modular surfaces
• Teichmüller curves in genus two: The decagon and beyond
• Veech surfaces and complete periodicity in genus two
• Geometry of infinitely generated Veech groups