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Spectral estimates for Ruelle transfer operators with two parameters and applications
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| hal.structure.identifier | School of Mathematics and Statistics [Crawley, Perth] | |
| dc.contributor.author | STOYANOV, Luchezar | |
| dc.date.accessioned | 2024-04-04T03:20:50Z | |
| dc.date.available | 2024-04-04T03:20:50Z | |
| dc.date.created | 2014-09-02 | |
| dc.date.issued | 2016-11-14 | |
| dc.identifier.issn | 1078-0947 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194617 | |
| dc.description.abstractEn | For $C^2$ weak mixing Axiom A flow $\phi_t: M \longrightarrow M$ on a Riemannian manifold $M$ and a basic set $\Lambda$ for $\phi_t$ we consider the Ruelle transfer operator $L_{f - s \tau + z g}$, where $f$ and $g$ are real-valued Hölder functions on $\Lambda$, $\tau$ is the roof function and $s, z$ are complex parameters. Under some assumptions about $\phi_t$ we establish estimates for the iterations of this Ruelle operator in the spirit of the estimates for operators with one complex parameter (see \cite{D}, \cite{St2}, \cite{St3}). Two cases are covered: (i) for arbitrary Hölder $f,g$ when $|\Im z| \leq B |\Im s|^\mu$ for some constants $B > 0$, $0 < \mu < 1$ ($\mu = 1$ for Lipschitz $f,g$), (ii) for Lipschitz $f,g$ when $|\Im s| \leq B_1 |\Im z|$ for some constant $B > 0$ . Applying these estimates, we obtain a non zero analytic extension of the zeta function $\zeta(s, z)$ for $P_f - \epsilon < \Re (s) < P_f$ and $|z|$ small enough with simple pole at $s = s(z)$. Two other applications are considered as well: the first concerns the Hannay-Ozorio de Almeida sum formula, while the second deals with the asymptotic of the counting function $\pi_F(T)$ for weighted primitive periods of the flow $\phi_t.$ | |
| dc.description.sponsorship | Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution - ANR-11-BS01-0019 | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.title.en | Spectral estimates for Ruelle transfer operators with two parameters and applications | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.identifier.arxiv | 1409.0721 | |
| bordeaux.journal | Discrete and Continuous Dynamical Systems - Series A | |
| bordeaux.page | 6413-6451. | |
| bordeaux.volume | 36 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 11 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01060131 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01060131v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Discrete%20and%20Continuous%20Dynamical%20Systems%20-%20Series%20A&rft.date=2016-11-14&rft.volume=36&rft.issue=11&rft.spage=6413-6451.&rft.epage=6413-6451.&rft.eissn=1078-0947&rft.issn=1078-0947&rft.au=PETKOV,%20Vesselin&STOYANOV,%20Luchezar&rft.genre=article |
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