Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies

Details Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies

2003-06-02

arxiv.org/abs/math/0306041v2

Mathematics

Dynamical Systems

10 pages, 2 figures. This is an extended version of the paper "Hyperbolicity of periodic points for horseshoes with internal t

Scientific paper

We study the hyperbolicity of a class of horseshoes exhibiting an internal
tangency, i.e. a point of homoclinic tangency accumulated by periodic points.
In particular these systems are strictly not uniformly hyperbolic. However we
show that all the Lyapunov exponents of all invariant measures are uniformly
bounded away from 0. This is the first known example of this kind.

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