Billiards on rational-angled triangles

By Richard Kenyon, J. Smillie. 2000

161 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9fca8902679d47c372fafe3efe55b1c776b300ae

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Citations in the corpus

INFINITELY GENERATED VEECH GROUPS (2004, methodology): “Thus, by Theorem 28 of [ KS ] the holonomy field of the surface is Q( p 5).”
On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus (2009, background): “There is natural invariant we can associate to a flat surface with a pseudo-Anosov homeomorphism φ: this is the trace field (see [14]), the number field generated by λ(φ) + 1 λ(φ) .”
Teichmüller curves in genus two: The decagon and beyond (2005, unknown): “For additional background on Teichm¨uller curves, see [Th], [V1], [V2], [Vo], [Wa], [ KS ], [Pu], [GJ], [EO], [Lei] and [Lo].”
The field of definition of affine invariant submanifolds of the moduli space of abelian differentials (2012, background): “2;R/–orbit, the absolute and relative periods span the same Q–vector subspace of C ; see Kenyon and Smillie [18] and [24].”
Euler characteristics of Teichmüller curves in genus two (2006, methodology): “f the primitive Teichmu¨ller curves in M2 generated by an Abelian diﬀerential. Teichmu¨ller curves in genus two were also studied by Calta in [Cal04], using the Kenyon-Smillie invariant introduced in [KS00]. 13 Associated to every known SL2Rorbit closure in Ω1Mg is a canonical ﬁnite, ergodic measure”
Prym Varieties and Teichmüller Curves (2006, background): “2. The periods of ω span a 2-dimensional vector space over K. See [ KS , Appendix], [Mc3, §9].”
Grid graphs and lattice surfaces (2008, background): “3, §3] for further background on this subject. Lemma 36. Suppose that Γ = PSL(X,ω) is ﬁnitely generated and non-elementary. Then kΓ = Q(tr Γ). This lemma is follows from results of Kenyon and Smillie [KS00]. Hubert and Schmidt realized that the following is implied by theorem 28 of [KS00]. Theorem 3”
Cylinder deformations in orbit closures of translation surfaces (2013, background): “The key tool is the result of Smillie and Weiss [23] mentioned above.”
Generalized Staircases: Recurrence and Symmetry (2009, methodology): “We will follow the treatment of the holonomy field given in the appendix of [10].”
Teichmüller curves in genus two: Discriminant and spin (2005, background): “See [EMS] and [HL] for additional results on the curves Wd2, and [V1], [V2], [Vo], [Wa], [ KS ], [Pu], [GJ], [EO], and [Ca] for more on Teichm¨uller curves.”