Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities
Dynamical Systems
2020-04-21 v2
Abstract
This work constructs symbolic dynamics for non-uniformly hyperbolic surface maps with a set of discontinuities . We allow the derivative of points nearby to be unbounded, of the order of a negative power of the distance to . Under natural geometrical assumptions on the underlying space , we code a set of non-uniformly hyperbolic orbits that do not converge exponentially fast to . The results apply to non-uniformly hyperbolic planar billiards, e.g. Bunimovich stadia.
Cite
@article{arxiv.1606.05863,
title = {Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities},
author = {Yuri Lima and Carlos Matheus},
journal= {arXiv preprint arXiv:1606.05863},
year = {2020}
}
Comments
36 pages, 1 figure, to appear in Ann. Sci. \'Ec. Norm. Sup\'er