Disintegration of invariant measures for hyperbolic skew products

DOI10.1007/s11856-017-1477-zzbMath1379.37053arXiv1503.04319OpenAlexW2964001953MaRDI QIDQ2357004

Ian Melbourne, Oliver Butterley

Publication date: 7 June 2017

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.04319

zbMATH Keywords

SRB measuredisintegration of a measurehyperbolic skew product

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) Integration and disintegration of measures (28A50)

Related Items (10)

Exponential decay of correlations for nonuniformly hyperbolic flows with a \(C^{1+\alpha}\) stable foliation, including the classical Lorenz attractor ⋮ Renewal theorems and mixing for non Markov flows with infinite measure ⋮ Robust exponential mixing and convergence to equilibrium for singular-hyperbolic attracting sets ⋮ Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps ⋮ Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps ⋮ Erratum to: ``Robust exponential decay of correlations for singular-flows ⋮ Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps ⋮ Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps ⋮ Extensions with shrinking fibers ⋮ Open sets of exponentially mixing Anosov flows

Cites Work

• Robust exponential decay of correlations for singular-flows
• Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
• Exponential mixing for the Teichmüller flow
• Open sets of Axiom A flows with exponentially mixing attractors
• Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence
• Singular-hyperbolic attractors are chaotic
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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