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Veech (or lattice) surfaces
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Veech Groups, Cutting Sequences, and Penetration Spectra - C. Ulcigrai
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- 1 Introduzione
- 2 Translation surfaces Translation surfaces are obtained by glueing polygons with pairs of parallel sides identified by translations
- 3 Affine automorphisms and Veech groups Definition (Affine diffeomorphisms) A diffeomorphism S S between translation surfaces S. S' is affine iff it is affine in each chart and Du(z) is independent onz…
- 4 Veech (or lattice) surfaces
- 5 Cutting sequences of linear trajectories Givena a polygonal presentation of a (Veech) translation surface, label by an alphabet A pairs of glued sides
- 6 Brief history of cutting sequences characterizations
- 7 A characterization of Sturmian sequences via substitutions
- 8 Properties of the classical Lagrange spectrum
- 9 Hallray for Veech translation surfaces We generalize the result by Hall to any Veech translation surface
- 10 Affine deformations and Teichmueller curves Let S be a Veech surface (V(56) is a lattice)
- 11 Ideas of proofs of cutting sequences characterizations
- 12 The octagon: other transitions diagrams The action of gives labels permutations and transition diagrams D, for
- 13 Derived sequences Definition The derived sequence of an admissible quence is obtained by keeping followed by the same letter Example
- 14 Geometric interpreation of derivation for the octagon
- 15 Renormalization on the octagon Teichmüller disk
- 16 Bouw-Moeller derivation Given a cutting sequence w for Sa... we define a combinatorial derivation
- 17 Renormalization on the Bouw Moeller Teichmüller disk
- 18 Hall Rays in Lagrange Spectra of Veech surfaces Let S be a Veech surface. Consider a fundamental domain for V(5)
- 19 Hall Rays in Lagrange Spectra of Veech surfaces Let S be a Veech surface. Consider a fundamental domain for V(S).
- 20 Boundary expansions and wedges of saddle connections
