Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies
Dynamical Systems
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0306041,
title = {Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies},
author = {Yongluo Cao and Stefano Luzzatto and Isabel Rios},
journal= {arXiv preprint arXiv:math/0306041},
year = {2007}
}
Comments
10 pages, 2 figures. This is an extended version of the paper "Hyperbolicity of periodic points for horseshoes with internal tangencies" by S. Luzzatto and I. Rios