Exponential mixing for generic volume-preserving Anosov flows in dimension three

DOI10.2969/JMSJ/07027595zbMath1393.37028arXiv1601.00063OpenAlexW2962906663WikidataQ115489114 ScholiaQ115489114MaRDI QIDQ1651448

Masato Tsujii

Publication date: 12 July 2018

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

Full work available at URL: https://arxiv.org/abs/1601.00063

zbMATH Keywords

transfer operatordecay of correlationsAnosov flow

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (14)

The work of Sébastien Gouëzel on limit theorems and on weighted Banach spaces ⋮ Mixing properties of generalized \(T,T^{-1}\) transformations ⋮ Limit theorems for fast-slow partially hyperbolic systems ⋮ Superpolynomial and polynomial mixing for semiflows and flows ⋮ Polynomial decay of correlations for flows, including Lorentz gas examples ⋮ Global normal form and asymptotic spectral gap for open partially expanding maps ⋮ Rates of mixing for non-Markov infinite measure semiflows ⋮ Exponential decay of correlations for Gibbs measures and semiflows over \(C^{1+\alpha }\) piecewise expanding maps ⋮ First band of Ruelle resonances for contact Anosov flows in dimension 3 ⋮ Spectral theory of the frame flow on hyperbolic 3-manifolds ⋮ Open sets of exponentially mixing Anosov flows ⋮ On the rate of mixing of circle extensions of Anosov maps ⋮ Horocycle averages on closed manifolds and transfer operators ⋮ Smooth mixing Anosov flows in dimension three are exponentially mixing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exponential decay of correlations for piecewise cone hyperbolic contact flows
• Markov approximations and decay of correlations for Anosov flows
• On decay of correlations in Anosov flows
• Pseudodifferential operators and nonlinear PDE
• A measure on the space of smooth mappings and dynamical system theory
• Exponential decay of correlations for finite horizon Sinai billiard flows
• On contact Anosov flows
• The semiclassical zeta function for geodesic flows on negatively curved manifolds
• Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
• Stability of mixing and rapid mixing for hyperbolic flows
• Banach spaces adapted to Anosov systems
• Prequantum transfer operator for symplectic Anosov diffeomorphism
• Quasi-compactness of transfer operators for contact Anosov flows
• Prevalence of rapid mixing in hyperbolic flows
• Prevalence of rapid mixing—II: topological prevalence
• Contact Anosov flows and the Fourier–Bros–Iagolnitzer transform
• On the Volume Elements on a Manifold
• Large deviations
• An introduction to semiclassical and microlocal analysis

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