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arXiv · 1606.05863

Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities

Yuri Lima·Carlos Matheus
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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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Yuri Lima, Carlos Matheus. 2016-06-19. Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities. https://doi.org/10.24033/asens.2349

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