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.
Mots-clés : Positive Lyapunov exponents, Gibbs–Markov–Young structure
@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}, pages = {101--120}, publisher = {Elsevier}, volume = {30}, number = {1}, year = {2013}, doi = {10.1016/j.anihpc.2012.06.004}, mrnumber = {3011293}, zbl = {06154084}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.004/} }
TY - JOUR AU - Alves, José F. AU - Dias, Carla L. AU - Luzzatto, Stefano TI - Geometry of expanding absolutely continuous invariant measures and the liftability problem JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 101 EP - 120 VL - 30 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.004/ DO - 10.1016/j.anihpc.2012.06.004 LA - en ID - AIHPC_2013__30_1_101_0 ER -
%0 Journal Article %A Alves, José F. %A Dias, Carla L. %A Luzzatto, Stefano %T Geometry of expanding absolutely continuous invariant measures and the liftability problem %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 101-120 %V 30 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.004/ %R 10.1016/j.anihpc.2012.06.004 %G en %F 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) no. 1, pp. 101-120. doi : 10.1016/j.anihpc.2012.06.004. http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.004/
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