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arXiv · 0908.4293

Non-hyperbolic ergodic measures with large support

Ch. Bonatti·L. J. Diaz·A. Gorodetski
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Abstract

We prove that there is a residual subset $\mathcal{S}$ in $\text{Diff}^1(M)$ such that, for every $f\in \mathcal{S}$, any homoclinic class of $f$ with invariant one dimensional central bundle containing saddles of different indices (i.e. with different dimensions of the stable invariant manifold) coincides with the support of some invariant ergodic non-hyperbolic (one of the Lyapunov exponents is equal to zero) measure of $f$.

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Ch. Bonatti, L. J. Diaz, A. Gorodetski. 2009-08-28. Non-hyperbolic ergodic measures with large support. https://doi.org/10.1088/0951-7715%2F23%2F3%2F015

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