%0 Journal Article
%T SRB measures for partially hyperbolic systems whose central direction is weakly expanding
%A Jose F. Alves
%A C. L. Dias
%A S. Luzzatto
%A V. Pinheiro
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1403.2937v2