Geometry of expanding absolutely continuous invariant measures and the liftability problem
Alves, José F. ; Dias, Carla L. ; Luzzatto, Stefano
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013), p. 101-120 / Harvested from Numdam
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We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs–Markov–Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of an invariant probability measure which is absolutely continuous measure (with respect to Lebesgue) and for which all Lyapunov exponents are positive.

Publié le : 2013-01-01
DOI : https://doi.org/10.1016/j.anihpc.2012.06.004
Classification:  37A05,  37C40,  37D25 
@article{AIHPC_2013__30_1_101_0,
     author = {Alves, Jos\'e F. and Dias, Carla L. and Luzzatto, Stefano},
     title = {Geometry of expanding absolutely continuous invariant measures and the liftability problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {30},
     year = {2013},
     pages = {101-120},
     doi = {10.1016/j.anihpc.2012.06.004},
     mrnumber = {3011293},
     zbl = {06154084},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2013__30_1_101_0}
}

Alves, José F.; Dias, Carla L.; Luzzatto, Stefano. Geometry of expanding absolutely continuous invariant measures and the liftability problem. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) pp. 101-120. doi : 10.1016/j.anihpc.2012.06.004. http://gdmltest.u-ga.fr/item/AIHPC_2013__30_1_101_0/

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