Billiards in right triangles and orbit closures in genus zero strata

Abstract

The orbit closure of the unfolding of every rational right and isosceles triangle is computed and the asymptotic number of periodic billiard trajectories in these triangles is deduced. This follows by classifying all orbit closures of rank at least two in hyperelliptic components of strata of Abelian and quadratic differentials. Additionally, given a fixed set of angles, the orbit closure of the unfolding of all unit area rational parallelograms, isosceles trapezoids, and right trapezoids outside of a discrete set is determined.

arXiv comment92 pages. 12 figures. Comments welcome!

References in corpus (10)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
• Invariant and stationary measures for the SL(2,R) action on Moduli space
• Semisimplicity and rigidity of the Kontsevich-Zorich cocycle
• On triangular billiards
• Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle
• Marked points on translation surfaces
• Periodic Points in Genus Two: Holomorphic Sections over Hilbert Modular Varieties, Teichmuller Dynamics, and Billiards
• Reconstructing orbit closures from their boundaries
• Invariant Subvarieties of Minimal Homological Dimension, Zero Lyapunov Exponents, and Monodromy