Expanding measures
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 6, p. 889-939

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.

@article{AIHPC_2011__28_6_889_0,
author = {Pinheiro, Vilton},
title = {Expanding measures},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {28},
number = {6},
year = {2011},
pages = {889-939},
doi = {10.1016/j.anihpc.2011.07.001},
zbl = {1254.37026},
mrnumber = {2859932},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2011__28_6_889_0}
}

Pinheiro, Vilton. Expanding measures. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 6, pp. 889-939. doi : 10.1016/j.anihpc.2011.07.001. http://www.numdam.org/item/AIHPC_2011__28_6_889_0/

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