Equilibrium states for hyperbolic potentials via inducing schemes
Abstract
In a context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. This generalizes a result due to Ramos and Viana, where analytical methods are used for maps with no critical sets. The strategy here consists in using a finite number of inducing schemes with a Markov structure in infinitely many symbols to code the dynamics, to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map. We apply our results to the important class of multidimensional Viana maps.
Cite
@article{arxiv.2003.11620,
title = {Equilibrium states for hyperbolic potentials via inducing schemes},
author = {Jose F. Alves and Krerley Oliveira and Eduardo Santana},
journal= {arXiv preprint arXiv:2003.11620},
year = {2024}
}
Comments
We made substantial changes with respect to the structure of the presentation and the application part. We also changed the title