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

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

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

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arxiv 1804.05690 v4 pith:RM6UN2HB submitted 2018-04-16 math.GT math.DS

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 This is my paper

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keywords billiarddynamicsflatshapesymbolictablesaffinebounce

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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.

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

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