How to hear the shape of a billiard table
Dynamical Systems
2018-06-27 v1
Abstract
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods for reconstructing from the bounce spectrum of a polygonal billiard table both the cyclic ordering of its edge labels and the sizes of its angles. We also show that it is impossible to reconstruct the exact shape of a polygonal billiard table from any finite collection of finite words from its bounce spectrum.
Keywords
Cite
@article{arxiv.1806.09644,
title = {How to hear the shape of a billiard table},
author = {Aaron Calderon and Solly Coles and Diana Davis and Justin Lanier and Andre Oliveira},
journal= {arXiv preprint arXiv:1806.09644},
year = {2018}
}
Comments
40 pages, 19 figures