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arXiv · 1811.09936

SRB measures for some diffeomorphisms with dominated splittings as zero noise limits

Zeya Mi
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Abstract

In this paper, we provide a technique result on the existence of Gibbs cu-states for diffeomorphisms with dominated splittings. More precisely, for given $C^2$ diffeomorphim $f$ with dominated splitting $T_{\Lambda}M = E\oplus F$ on an attractor $\Lambda$, by considering some suitable random perturbation of $f$, we show that for any zero noise limit of ergodic stationary measures, if it has positive integrable Lyapunov exponents along invariant sub-bundle $E$, then its ergodic components contain Gibbs cu-states associated to $E$. With this technique, we show the existence of SRB measures and physical measures for some systems exhibitting dominated splittings and weak hyperbolicity.

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Zeya Mi. 2018-11-25. SRB measures for some diffeomorphisms with dominated splittings as zero noise limits. https://arxiv.org/abs/1811.09936

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