An expansion estimate for dispersing planar billiards with corner points
Dynamical Systems
2013-01-01 v1
Abstract
It is known that the dynamics of planar billiards satisfies strong mixing properties (e.g. exponential decay of correlations) provided that some expansion condition on unstable curves is satisfied. This condition has been shown to always hold for smooth dispersing planar billiards, but it needed to be assumed separately in the case of dispersing planar billiards with corner points. We prove that this expansion condition holds for any dispersing planar billiard with corner points, no cusps and bounded horizon.
Keywords
Cite
@article{arxiv.1212.6897,
title = {An expansion estimate for dispersing planar billiards with corner points},
author = {Jacopo De Simoi and Imre Péter Tóth},
journal= {arXiv preprint arXiv:1212.6897},
year = {2013}
}