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arXiv · 1403.2937

SRB measures for partially hyperbolic systems whose central direction is weakly expanding

Jose F. Alves·C. L. Dias·S. Luzzatto·V. Pinheiro
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Abstract

We consider partially hyperbolic \( C^{1+} \) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \( E^s\oplus E^{cu} \). Assuming the existence of a set of positive Lebesgue measure on which \( f \) satisfies a weak nonuniform expansivity assumption in the centre~unstable direction, we prove that there exists at most a finite number of transitive attractors each of which supports an SRB measure. As part of our argument, we prove that each attractor admits a Gibbs-Markov-Young geometric structure with integrable return times. We also characterize in this setting SRB measures which are liftable to Gibbs-Markov-Young structures.

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Jose F. Alves, C. L. Dias, S. Luzzatto, V. Pinheiro. 2014-03-12. SRB measures for partially hyperbolic systems whose central direction is weakly expanding. https://arxiv.org/abs/1403.2937

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