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 
@article{JEMS_2017_19_10_a1,
     author = {Jos\'e F. Alves and Carla L. Dias and Stefano Luzzatto and Vilton Pinheiro},
     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},
     number = {10},
     year = {2017},
     doi = {10.4171/jems/731},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/731/}
}
TY  - JOUR
AU  - José F. Alves
AU  - Carla L. Dias
AU  - Stefano Luzzatto
AU  - Vilton Pinheiro
TI  - SRB measures for partially hyperbolic systems whose central direction is weakly expanding
JO  - Journal of the European Mathematical Society
PY  - 2017
SP  - 2911
EP  - 2946
VL  - 19
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/731/
DO  - 10.4171/jems/731
ID  - JEMS_2017_19_10_a1
ER  - 
%0 Journal Article
%A José F. Alves
%A Carla L. Dias
%A Stefano Luzzatto
%A Vilton Pinheiro
%T SRB measures for partially hyperbolic systems whose central direction is weakly expanding
%J Journal of the European Mathematical Society
%D 2017
%P 2911-2946
%V 19
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/731/
%R 10.4171/jems/731
%F JEMS_2017_19_10_a1
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. http://geodesic.mathdoc.fr/articles/10.4171/jems/731/

Cité par Sources :