Volume lemmas for partially hyperbolic endomorphisms and applications
Dynamical Systems
2018-10-08 v1
Abstract
We consider partially hyperbolic attractors for non-singular endomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. We prove volume lemmas for both Lebesgue measure on the topological basin of the attractor and the SRB measure supported on the attractor.As a consequence under a mild assumption we prove exponential large deviation bounds for the convergence of Birkhoff averages associated to continuous observables with respect to the SRB measure.
Cite
@article{arxiv.1810.02751,
title = {Volume lemmas for partially hyperbolic endomorphisms and applications},
author = {Anderson Cruz and Giovane Ferreira and Paulo Varandas},
journal= {arXiv preprint arXiv:1810.02751},
year = {2018}
}
Comments
25 pages, 2 figures. arXiv admin note: text overlap with arXiv:1810.02743