Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows

DOI10.1090/memo/1404OpenAlexW2773407410MaRDI QIDQ5877466

Latchezar Stoyanov

Publication date: 13 February 2023

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.03103

zbMATH Keywords

periodic orbitsspectrumzeta functiondecay of correlationsAnosov flowRuelle transfer operatorcontraction operatorscontact flow

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Cites Work

• Unnamed Item
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• Ruelle transfer operators with two complex parameters and applications
• Exponential decay of correlations for nonuniformly hyperbolic flows with a \(C^{1+\alpha}\) stable foliation, including the classical Lorenz attractor
• Pollicott-Ruelle resonances for open systems
• Band structure of the Ruelle spectrum of contact Anosov flows
• Anosov flows and dynamical zeta functions
• A functional analytic approach to perturbations of the Lorentz gas
• Distribution of periods of closed trajectories in exponentially shrinking intervals
• Spectral analysis of the transfer operator for the Lorentz gas
• A local trace formula for Anosov flows
• Upper bound on the density of Ruelle resonances for Anosov flows
• Hölder foliations
• Exponential decay of correlations for piecewise cone hyperbolic contact flows
• Correlations for pairs of closed geodesics
• Exponential mixing for the Teichmüller flow
• Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties
• Banach spaces for piecewise cone-hyperbolic maps
• A stretched exponential bound on time correlations for billiard flows
• On the rate of mixing of Axiom A flows
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Resonances for axiom A flows
• Markov approximations and decay of correlations for Anosov flows
• On decay of correlations in Anosov flows
• The ergodic theory of axiom A flows
• Smoothness of horocycle foliations
• Statistical properties of dynamical systems with some hyperbolicity
• Recurrence times and rates of mixing
• Subexponential decay of correlations
• Ruelle zeta function at zero for surfaces
• Exponential decay of correlations for finite horizon Sinai billiard flows
• Equidistribution for standard pairs in planar dispersing billiard flows
• On contact Anosov flows
• Decay of correlations and dispersing billiards.
• Decay of correlations
• Pinching conditions, linearization and regularity of axiom A flows
• Decay of correlations for normally hyperbolic trapping
• Power spectrum of the geodesic flow on hyperbolic manifolds
• The semiclassical zeta function for geodesic flows on negatively curved manifolds
• Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
• Correlations of length spectra for negatively curved manifolds
• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• Stability of mixing and rapid mixing for hyperbolic flows
• Simplicity of Lyapunov spectra: a sufficient criterion
• Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows
• Open sets of Axiom A flows with exponentially mixing attractors
• Dynamical zeta functions for Anosov flows via microlocal analysis
• Regular decay of ball diameters and spectra of Ruelle operators for contact Anosov flows
• Non-integrability of open billiard flows and Dolgopyat-type estimates
• On the Hannay–Ozorio De Almeida Sum Formula
• Sharp polynomial bounds on the number of Pollicott–Ruelle resonances
• Spectra of Ruelle transfer operators for Axiom A flows
• Expanding maps on Cantor sets and analytic continuation of zeta functions
• Regularity of the Anosov splitting II
• Statistical properties of two-dimensional hyperbolic billiards
• Stochastic stability of Pollicott–Ruelle resonances
• Banach spaces adapted to Anosov systems
• Rapid decay of correlations for nonuniformly hyperbolic flows
• Stability of statistical properties in two-dimensional piecewise hyperbolic maps
• Quasi-compactness of transfer operators for contact Anosov flows
• Decay of correlations for slowly mixing flows
• Correlations for pairs of periodic trajectories for open billiards
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Exponential error terms for growth functions on negatively curved surfaces
• Prevalence of rapid mixing in hyperbolic flows
• Prevalence of non-Lipschitz Anosov foliations
• Regularity of the Anosov splitting and of horospheric foliations
• Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems
• Prevalence of rapid mixing—II: topological prevalence
• Quantitative Pesin theory for Anosov diffeomorphisms and flows
• Dimension product structure of hyperbolic sets
• Ergodic Attractors
• Symbolic Dynamics for Hyperbolic Flows
• Ruelle Perron Frobenius spectrum for Anosov maps
• Exponential decay of correlations for surface semi-flows without finite Markov partitions
• Ruelle's lemma and Ruelle zeta functions
• Precise counting results for closed orbits of Anosov flows
• Exponential mixing of frame flows for convex cocompact hyperbolic manifolds
• Sharp large deviations for some hyperbolic systems
• Lectures on Lyapunov Exponents
• GIBBS MEASURES IN ERGODIC THEORY
• Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$
• Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function
• Invariant manifolds
• Asymptotic expansions for closed orbits in homology classes.