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 | |
Publication status | Published - 21 Sep 2021 |