You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces

2018/04/16 by Duchin, Moon, Erlandsson, Viveka, Leininger, Christopher J. +1 · 1 citation
#37B10 #57M50 #58J50 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1804.05690

Abstract

We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tables that can have the same bounce spectrum are right-angled tables that differ by an affine map. The main tool is a new theorem that establishes that a flat cone metric is completely determined by the support of its Liouville current.

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• Flexible hyperbolic cone metrics on the genus 2 surface

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