Cutting sequences, regular polygons, and the Veech group

DOI10.1007/S10711-012-9724-2zbMath1351.37147arXiv1708.09552OpenAlexW2065514421MaRDI QIDQ1938051

Diana Davis

Publication date: 1 February 2013

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09552

zbMATH Keywords

Veech groupscutting sequencesregular polygons

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Combinatorial dynamics (types of periodic orbits) (37E15) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (6)

Cutting sequences on square-tiled surfaces ⋮ On cutting sequences of the \(L\)-shaped translation surface tiled by three squares ⋮ Anomalous dynamics in symmetric triangular irrational billiards ⋮ Survey lecture on billiards ⋮ You can hear the shape of a billiard table: symbolic dynamics and rigidity for flat surfaces ⋮ Diagonal changes for surfaces in hyperelliptic components

Cites Work

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• The geometry of Markoff numbers
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• Geodesic flow on the Teichmueller disk of the regular octagon, cutting sequences and octagon continued fractions maps
• Beyond Sturmian sequences: coding linear trajectories in the regular octagon
• Veech’s dichotomy and the lattice property
• Planar structures and billiards in rational polygons: the Veech alternative
• Periodic trajectories in the regular pentagon

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