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

Viveka Erlandsson, Moon Duchin, Christopher Leininger, Chandrika Sadanand

Research output: Contribution to journalArticle (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 languageEnglish
Pages (from-to)421-463
JournalCommentarii Mathematici Helvetici
Volume96
Issue number3
DOIs
Publication statusPublished - 21 Sep 2021

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