2000
DOI: 10.1016/s0012-9593(00)00101-4
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Abstract: JOSÉ FERREIRA ALVES SRB measures for non-hyperbolic systems with multidimensional expansion Annales scientifiques de l'É.N.S. 4 e série, tome 33, n o 1 (2000), p. 1-32 © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 2000, tous droits réservés. L'accès aux archives de la revue « Annales scientifiques de l'É.N.S. » (http://www. elsevier.com/locate/ansens) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/c… Show more

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Cited by 108 publications
(184 citation statements)
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“…The first difficulty here is to modify the standard partition (see, e.g., [25]) and obtain good estimates on points with large return times. Here, a beautiful idea due to Alves [1] was instrumental. He studied (maps close to) a deterministic skew product T (x, θ) = (a − x 2 + εθ, Dθ mod 1) where D 1 gives a "strongly mixing" deterministic dynamical system on the circle.…”
Section: Informal Statement Of Resultsmentioning
confidence: 99%
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“…The first difficulty here is to modify the standard partition (see, e.g., [25]) and obtain good estimates on points with large return times. Here, a beautiful idea due to Alves [1] was instrumental. He studied (maps close to) a deterministic skew product T (x, θ) = (a − x 2 + εθ, Dθ mod 1) where D 1 gives a "strongly mixing" deterministic dynamical system on the circle.…”
Section: Informal Statement Of Resultsmentioning
confidence: 99%
“…He also exploited bounds on "exceptional sets" previously obtained by Viana [24], who was the first to study this skew product model and proved that it possesses two positive Lyapunov exponents. Although we consider a slightly more general framework than the Misiurewicz setting in [1] and [24], many properties become easier to prove in our i.i.d. setting (see Lemma 7.4, where we obtain exponential estimates, to be contrasted with the stretched exponential bounds in [24]).…”
Section: Informal Statement Of Resultsmentioning
confidence: 99%
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“…Alves [2] proved that they admit an absolutely continuous (physical, SRB) invariant probability measure which is mixing. (Viana [96] also studied the Lyapunov exponents of higher-dimensional invertible systems with multidimensional nonuniform hyperbolicity, replacing in particular a − x 2 by a Hénon map and Dθ by a hyperbolic solenoid.…”
Section: Low-dimensional Nonuniformly Hyperbolic Dynamics: Unimodal Mmentioning
confidence: 99%