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Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities

Authors
  • Lima, Yuri
  • Matheus, Carlos
Type
Preprint
Publication Date
Jun 19, 2016
Submission Date
Jun 19, 2016
Identifiers
arXiv ID: 1606.05863
Source
arXiv
License
Yellow
External links

Abstract

This work constructs symbolic dynamics for non-uniformly hyperbolic surface maps with a set of discontinuities $D$. We allow the derivative of points nearby $D$ to be unbounded, of the order of a negative power of the distance to $D$. Under natural geometrical assumptions on the underlying space $M$, we code a set of non-uniformly hyperbolic orbits that do not converge exponentially fast to $D$. The results apply to non-uniformly hyperbolic planar billiards, e.g. Bunimovich stadia.

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