Expanding measures

Pinheiro, Vilton

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011), p. 889-939 / Harvested from Numdam

Résumé

We prove that any $ {C}^{1+\alpha }$ transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion condition. This is an extension to arbitrary dimension of a famous theorem of Keller (1990) [33] for maps of the interval with negative Schwarzian derivative.Given a non-uniformly expanding set, we also show how to construct a Markov structure such that any invariant measure defined on this set can be lifted. We used these structure to study decay of correlations and others statistical properties for general expanding measures.

Détail

Publié le : 2011-01-01

MR 2859932 | Zbl 1254.37026 | 4 citations dans Numdam

DOI : https://doi.org/10.1016/j.anihpc.2011.07.001

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