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

Moon Duchin; Viveka Erlandsson; Christopher J. Leininger; Chandrika Sadanand

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arXiv · 1804.05690

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

Moon Duchin·Viveka Erlandsson·Christopher J. Leininger·Chandrika Sadanand

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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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Moon Duchin, Viveka Erlandsson, Christopher J. Leininger, Chandrika Sadanand. 2018-04-16. You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces. https://arxiv.org/abs/1804.05690

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