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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPETKOV, Vesselin
hal.structure.identifierThe University of Western Australia [UWA]
dc.contributor.authorSTOYANOV, Luchezar
dc.date.accessioned2024-04-04T02:55:48Z
dc.date.available2024-04-04T02:55:48Z
dc.date.created2020-11-10
dc.date.issued2020
dc.identifier.issn1424-0637
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192398
dc.description.abstractEnFor hyperbolic flows $\varphi_t$ we examine the Gibbs measure of points $w$ for which $$\int_0^T G(\varphi_t w) dt - a T \in (- e^{-\epsilon n}, e^{- \epsilon n})$$ as $n \to \infty$ and $T \geq n$, provided $\epsilon > 0$ is sufficiently small. This is similar to local central limit theorems. The fact that the interval $(- e^{-\epsilon n}, e^{- \epsilon n})$ is exponentially shrinking as $n \to \infty$ leads to several difficulties. Under some geometric assumptions we establish a sharp large deviation result with leading term $C(a) \epsilon_n e^{\gamma(a) T}$ and rate function $\gamma(a) \leq 0.$ The proof is based on the spectral estimates for the iterations of the Ruelle operators with two complex parameters and on a new Tauberian theorem for sequence of functions $g_n(t)$ having an asymptotic as $ n \to \infty$ and $t \geq n.$
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enhyperbolic flows
dc.subject.enlarge deviations
dc.subject.enTauberian theorem for sequence of functions
dc.title.enSharp large deviations for hyperbolic flows
dc.typeArticle de revue
dc.identifier.doi10.1007/s00023-020-00956-8
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv2002.11007v3
bordeaux.journalAnnales Henri Poincaré
bordeaux.page3791-3834
bordeaux.volume21
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue12
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02498740
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02498740v1
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