2018/10/05 by Anderson Cruz, Cruz, Anderson, Giovane Ferreira +3
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1810.02751
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.