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

Viveka Erlandsson; Moon Duchin; Christopher Leininger; Chandrika Sadanand

doi:10.4171/CMH/516

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

Viveka Erlandsson, Moon Duchin, Christopher Leininger, Chandrika Sadanand

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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.

Original language	English
Pages (from-to)	421-463
Journal	Commentarii Mathematici Helvetici
Volume	96
Issue number	3
DOIs	https://doi.org/10.4171/CMH/516
Publication status	Published - 21 Sep 2021

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https://arxiv.org/abs/1804.05690

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Dr Viveka Erlandsson
- v.erlandssonbristol.acuk
- School of Mathematics - Associate Professor
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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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AU - Sadanand, Chandrika

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AB - 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.

U2 - 10.4171/CMH/516

DO - 10.4171/CMH/516

M3 - Article (Academic Journal)

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JO - Commentarii Mathematici Helvetici

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

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