Exponential mixing for singular skew-products

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems with singularities (billiards, etc.) (37C83)

Cites Work

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Exponential decay of correlations for nonuniformly hyperbolic flows with a \(C^{1+\alpha}\) stable foliation, including the classical Lorenz attractor
Area expanding \({\mathcal C^{1+\alpha}}\) suspension semiflows
From rates of mixing to recurrence times via large deviations
On mixing properties of compact group extensions of hyperbolic systems
Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
Open sets of exponentially mixing Anosov flows
The Lorenz attractor is mixing
Exponential mixing for the Teichmüller flow
Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences
On the rate of mixing of Axiom A flows
On decay of correlations in Anosov flows
Statistical properties of dynamical systems with some hyperbolicity
Recurrence times and rates of mixing
SRB measures for partially hyperbolic systems whose central direction is mostly expanding
Exponential mixing for generic volume-preserving Anosov flows in dimension three
Statistical properties for flows with unbounded roof function, including the Lorenz attractor
Absolutely continuous invariant measures for multidimensional expanding maps
Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps
Inducing schemes for multi-dimensional piecewise expanding maps
Quantitative statistical properties of two-dimensional partially hyperbolic systems
Disintegration of invariant measures for hyperbolic skew products
Polynomial decay of correlations for flows, including Lorentz gas examples
Markov structures and decay of correlations for non-uniformly expanding dynamical systems
Exponential decay of correlations for surface semiflows with an expanding direction
Exponential mixing for skew products with discontinuities
Skew products, quantitative recurrence, shrinking targets and decay of correlations
Stretched-exponential mixing for skew products with discontinuities
Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence
Decay of correlations for nonuniformly expanding systems
Prevalence of non-Lipschitz Anosov foliations
Quantitative statistical stability, speed of convergence to equilibrium and partially hyperbolic skew products
Exponential decay of correlations for surface semi-flows without finite Markov partitions
Existence and smoothness of the stable foliation for sectional hyperbolic attractors
Decay of correlations in suspension semi-flows of angle-multiplying maps
Livšic regularity for Markov systems

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