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You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces by Duchin, Moon; Erlandsson, Viveka; Leininger, Christopher J.; Sadanand, Chandrika is a scholarly article available to read on EtoBox.

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

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.

Author

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

Published

2018

Language

EN