2005
DOI: 10.1016/j.anihpc.2004.12.002
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Markov structures and decay of correlations for non-uniformly expanding dynamical systems

Abstract: We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure. Moreover, the decay of the return time function can be controlled in terms of the time generic points need to achieve some uniform expanding behavior. As a consequence we obtain some rates for the decay of correlations of those maps and conditions for the validity of the Ce… Show more

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Cited by 90 publications
(144 citation statements)
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“…The integrability properties of this first hyperbolic time map play an important role in the study of some statistical properties of several classes of dynamical systems, such as stochastic stability and decay of correlations; see [2,4,5,9]. The same conclusion of Theorem A can be obtained under the assumption of integrability with respect to Lebesgue measure of the first hyperbolic time map.…”
Section: Statement Of Resultssupporting
confidence: 63%
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“…The integrability properties of this first hyperbolic time map play an important role in the study of some statistical properties of several classes of dynamical systems, such as stochastic stability and decay of correlations; see [2,4,5,9]. The same conclusion of Theorem A can be obtained under the assumption of integrability with respect to Lebesgue measure of the first hyperbolic time map.…”
Section: Statement Of Resultssupporting
confidence: 63%
“…These have become a very useful ingredient in the study of non-hyperbolic dynamical systems, playing an important role in the proof of several results about the existence of absolutely continuous invariant measures and their statistical properties; see [1,2,3,4,5,6]. Ideas of hyperbolic times were implicitly contained in Pesin's theory and in the work of Pliss and Mañé.…”
Section: Introductionmentioning
confidence: 99%
“…Results in [7,29] show that the tail set decays at least sub-exponentially fast, which is not enough to ensure that Corollaries C and E are true for the maps in U ∪Ũ. It is conjectured that the tail set indeed decays exponentially fast and with a uniform rate for all maps in U ∪Ũ.…”
Section: Viana Mapsmentioning
confidence: 99%
“…Then for the same kind of attracting sets we obtain an upper bound for the subset corresponding to (7). Theorem D. Let f : M → M be a C 2 diffeomorphism exhibiting a partially hyperbolic non-uniformly expanding attracting set Λ with isolating neighborhood U ⊃ Λ.…”
mentioning
confidence: 99%
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