Erratum to: Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

Araújo, Vı́tor; Galatolo, Stefano; Pacífico, Maria José

doi:10.1007/s00209-015-1613-6

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Upper Bound For Large Deviations1

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2018

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“…In addition, recent results obtained in [9,10] depend on the skew-product representation of a global Poincaré map given by Theorem 2.8 (corresponding to [9,Theorem 5] ensuring the application of [9, Theorem A and Proposition 1] to singular-hyperbolic attractors), which now holds without assuming transitivity or that all equilibria are non-resonant Lorenz-like singularities for 3-dimensional vector fields only.…”

Section: Upper Bound For Large Deviationsmentioning

confidence: 99%

Upper Large Deviations Bound for Singular-Hyperbolic Attracting Sets

2018

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We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities and/or discontinuities, where the roof function defining the suspension behaves like the logarithm of the distance to the singular/discontinuous set of the base map. To obtain this upper bound, we show that the base transformation exhibits exponential slow recurrence to the singular set.The results are applied to semiflows modeling singular-hyperbolic attracting sets of C 2 vector fields. As corollary of the methods we obtain results on the existence of physical measures and their statistical properties for classes of piecewise C 1+ expanding maps of the interval with singularities and discontinuities. We are also able to obtain exponentially fast escape rates from subsets without full measure.

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Section: Upper Bound For Large Deviationsmentioning

confidence: 99%