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arXiv · 1810.02751

Volume lemmas for partially hyperbolic endomorphisms and applications

Anderson Cruz·Giovane Ferreira·Paulo Varandas
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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.

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Anderson Cruz, Giovane Ferreira, Paulo Varandas. 2018-10-05. Volume lemmas for partially hyperbolic endomorphisms and applications. https://arxiv.org/abs/1810.02751

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