Geodesic
SRB measures for partially hyperbolic systems whose central direction is weakly expanding
Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2911-2946

Voir la notice de l'article provenant de la source EMS Press

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 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.
DOI : 10.4171/jems/731
Classification : 37-XX
Keywords: SRB measures, Lyapunov exponents, Nonuniform expansion, GMY structures 
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     title = {SRB measures for partially hyperbolic systems whose central direction is weakly expanding},
     journal = {Journal of the European Mathematical Society},
     pages = {2911--2946},
     publisher = {mathdoc},
     volume = {19},
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     year = {2017},
     doi = {10.4171/jems/731},
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José F. Alves; Carla L. Dias; Stefano Luzzatto; Vilton Pinheiro. SRB measures for partially hyperbolic systems whose central direction is weakly expanding. Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2911-2946. doi: 10.4171/jems/731

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