Ruelle transfer operators with two complex parameters and applications

DOI10.3934/dcds.2016077zbMath1366.37055OpenAlexW2509750681MaRDI QIDQ325253

Vesselin Petkov, Latchezar Stoyanov

Publication date: 18 October 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016077

zbMATH Keywords

zeta functionAxiom A flowbasic setperiods counting functionRuelle transfer operator

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Orbit growth in dynamical systems (37C35) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Closed orbits in homology classes
• An extension of the theory of Fredholm determinants
• Large deviations, fluctuations and shrinking intervals
• On the rate of mixing of Axiom A flows
• Distribution of periodic orbits of symbolic and axiom A flows
• On decay of correlations in Anosov flows
• The ergodic theory of axiom A flows
• Synchronization of canonical measures for hyperbolic attractors
• Large deviation asymptotics for Anosov flows
• Pinching conditions, linearization and regularity of axiom A flows
• Ruelle operators with two complex parameters and applications
• Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows
• On the Hannay–Ozorio De Almeida Sum Formula
• Spectra of Ruelle transfer operators for Axiom A flows
• Expanding maps on Cantor sets and analytic continuation of zeta functions
• Exponential error terms for growth functions on negatively curved surfaces
• Symbolic Dynamics for Hyperbolic Flows
• Ruelle's lemma and Ruelle zeta functions
• Sharp large deviations for some hyperbolic systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms