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- Title
SRB measures for partially hyperbolic systems whose central direction is weakly expanding.
- Authors
Alves, José F.; Dias, Carla L.; Luzzatto, Stefano; Pinheiro, Vilton
- Abstract
We consider partially hyperbolic C1+ diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition Es ⊕. Ecu. 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 exist 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.
- Subjects
DIFFEOMORPHISMS; HYPERBOLIC groups; RIEMANNIAN manifolds; DIMENSION theory (Algebra); LEBESGUE measure
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2017, Vol 19, Issue 10, p2911
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/731