Comptes Rendus
no. 13-14
Mathematical Analysis/Dynamical Systems
Sharp large deviations for some hyperbolic flows
[Larges déviations exactes pour certains flots hyperboliques]

Présenté par : the Editorial Board

Vesselin Petkov1 ; Luchezar Stoyanov2
1 Université Bordeaux I, institut de mathématiques, 351, cours de la Libération, 33405 Talence, France
2 University of Western Australia, School of Mathematics and Statistics, Perth, WA 6009, Australia
Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 665-669.

On justifie le principe de larges déviations exactes avec des intervalles décroissants sub-exponentiellement pour certains modèles concernant lʼapplication de Poincaré associée à une famille de Markov pour un Axiom A flot restreint à un ensemble basique qui satisfait des conditions de régularité additionnelles.

We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincaré map related to a Markov family for an Axiom A flow restricted to a basic set satisfying some additional regularity assumptions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.07.012
Vesselin Petkov 1 ; Luchezar Stoyanov 2

1 Université Bordeaux I, institut de mathématiques, 351, cours de la Libération, 33405 Talence, France
2 University of Western Australia, School of Mathematics and Statistics, Perth, WA 6009, Australia 
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Vesselin Petkov; Luchezar Stoyanov. Sharp large deviations for some hyperbolic flows. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 665-669. doi : 10.1016/j.crma.2012.07.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.012/

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[6] M. Pollicott; R. Sharp Large deviations, fluctuations and shrinking intervals, Comm. Math. Phys., Volume 290 (2009), pp. 321-334

[7] L. Ray-Bellet; L.-S. Young Large deviations in non-uniformly hyperbolic dynamical systems, Ergodic Theory Dynam. Systems, Volume 28 (2008), pp. 587-612

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