[Larges déviations exactes pour certains flots hyperboliques]
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.
Accepté le :
Publié le :
@article{CRMATH_2012__350_13-14_665_0,
author = {Petkov, Vesselin and Stoyanov, Luchezar},
title = {Sharp large deviations for some hyperbolic flows},
journal = {Comptes Rendus. Math\'ematique},
pages = {665--669},
publisher = {Elsevier},
volume = {350},
number = {13-14},
year = {2012},
doi = {10.1016/j.crma.2012.07.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.07.012/}
}
TY - JOUR AU - Petkov, Vesselin AU - Stoyanov, Luchezar TI - Sharp large deviations for some hyperbolic flows JO - Comptes Rendus. Mathématique PY - 2012 SP - 665 EP - 669 VL - 350 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.07.012/ DO - 10.1016/j.crma.2012.07.012 LA - en ID - CRMATH_2012__350_13-14_665_0 ER -
%0 Journal Article %A Petkov, Vesselin %A Stoyanov, Luchezar %T Sharp large deviations for some hyperbolic flows %J Comptes Rendus. Mathématique %D 2012 %P 665-669 %V 350 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.07.012/ %R 10.1016/j.crma.2012.07.012 %G en %F CRMATH_2012__350_13-14_665_0
Petkov, Vesselin; Stoyanov, Luchezar. Sharp large deviations for some hyperbolic flows. Comptes Rendus. Mathématique, Tome 350 (2012) no. 13-14, pp. 665-669. doi : 10.1016/j.crma.2012.07.012. http://www.numdam.org/articles/10.1016/j.crma.2012.07.012/
[1] Symbolic dynamics for hyperbolic flows, Amer. J. Math., Volume 95 (1973), pp. 429-460
[2] On decay of correlations in Anosov flows, Ann. of Math., Volume 147 (1998), pp. 357-390
[3] Large deviations in dynamical systems and stochastic processes, Trans. Amer. Math. Soc., Volume 321 (1990), pp. 505-524
[4] Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, Volume 187–188 (1990)
[5] Sharp large deviations for some hyperbolic systems, 2012 (preprint) | arXiv
[6] Large deviations, fluctuations and shrinking intervals, Comm. Math. Phys., Volume 290 (2009), pp. 321-334
[7] Large deviations in non-uniformly hyperbolic dynamical systems, Ergodic Theory Dynam. Systems, Volume 28 (2008), pp. 587-612
[8] Spectra of Ruelle transfer operators for Axiom A flows on basic sets, Nonlinearity, Volume 24 (2011), pp. 1089-1120
[9] Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows, Proc. Amer. Math. Soc., Volume 140 (2012), pp. 3463-3478
[10] Large deviation asymptotics for Anosov flows, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 13 (1996), pp. 445-484
[11] Large deviations in dynamical systems, Trans. Amer. Math. Soc., Volume 318 (1990), pp. 525-543
Cité par Sources :
