Corpus ID: 73600757

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

@article{Duchin2018YouCH,
  title={You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces},
  author={Moon Duchin and Viveka Erlandsson and C. Leininger and Chandrika Sadanand},
  journal={arXiv: Geometric Topology},
  year={2018}
}
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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