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arXiv · 0804.1796

Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes

Lorenzo J. Diaz·Anton Gorodetski
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Abstract

We prove that for a generic $C^1$-diffeomorphism existence of a homoclinic class with periodic saddles of different indices (dimension of the unstable bundle) implies existence an invariant ergodic non-hyperbolic (one of the Lyapunov exponents is equal to zero) measure of $f$.

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Lorenzo J. Diaz, Anton Gorodetski. 2008-04-10. Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes. https://arxiv.org/abs/0804.1796

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