Density of convex billiards with rational caustics
Dynamical Systems
2018-11-14 v2
Abstract
We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of rotation number is polynomial sense in the smooth case, and exponentially dense in the analytic case.
Keywords
Cite
@article{arxiv.1706.07968,
title = {Density of convex billiards with rational caustics},
author = {Vadim Kaloshin and Ke Zhang},
journal= {arXiv preprint arXiv:1706.07968},
year = {2018}
}
Comments
22 pages, corrections and clarifications added from last version