Martingale-coboundary decomposition for families of dynamical systems

DOI10.1016/j.anihpc.2017.08.005zbMath1406.37027arXiv1608.01853OpenAlexW2962844249WikidataQ57930956 ScholiaQ57930956MaRDI QIDQ1747351

Alexey Korepanov, Ian Melbourne, Zemer Kosloff

Publication date: 8 May 2018

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.01853

zbMATH Keywords

fast-slow systemsnonuniform hyperbolicityhomogenisationmartingale-coboundary decompositionstatistical limit laws

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical aspects of statistical mechanics (37A60) Systems with slow and fast motions for nonlinear problems in mechanics (70K70)

Related Items (23)

Almost sure invariance principle for non-autonomous holomorphic dynamics in ℙ^{𝕜} ⋮ Iterated invariance principle for slowly mixing dynamical systems ⋮ Deterministic homogenization under optimal moment assumptions for fast-slow systems. I ⋮ Deterministic homogenization under optimal moment assumptions for fast-slow systems. II ⋮ Flexibility of statistical properties for smooth systems satisfying the central limit theorem ⋮ On the timescale at which statistical stability breaks down ⋮ Superpolynomial and polynomial mixing for semiflows and flows ⋮ A vector-valued almost sure invariance principle for random expanding on average cocycles ⋮ Variance continuity for Lorenz flows ⋮ Large deviations, moment estimates and almost sure invariance principles for skew products with mixing base maps and expanding-on-average fibers ⋮ Existence and non-existence of solutions to the coboundary equation for measure-preserving systems ⋮ Statistical properties for flows with unbounded roof function, including the Lorenz attractor ⋮ Limit theorems for some time-dependent expanding dynamical systems ⋮ Rates of convergence in invariance principles for random walks on linear groups via martingale methods ⋮ Rates in almost sure invariance principle for slowly mixing dynamical systems ⋮ Rates in almost sure invariance principle for dynamical systems with some hyperbolicity ⋮ Equidistribution for nonuniformly expanding dynamical systems, and application to the almost sure invariance principle ⋮ Loss of memory and moment bounds for nonstationary intermittent dynamical systems ⋮ Rates in almost sure invariance principle for quickly mixing dynamical systems ⋮ Sharp statistical properties for a family of multidimensional nonMarkovian nonconformal intermittent maps ⋮ Rate of convergence in the weak invariance principle for deterministic systems ⋮ Limit theorems for random non-uniformly expanding or hyperbolic maps with exponential tails ⋮ Almost sure invariance principle for random dynamical systems via Gouëzel's approach

Cites Work

• Unnamed Item
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• Smooth approximation of stochastic differential equations
• Linear response for intermittent maps
• A functional analytic approach to perturbations of the Lorentz gas
• Moment bounds for dependent sequences in smooth Banach spaces
• From rates of mixing to recurrence times via large deviations
• An invariance principle for maps with polynomial decay of correlations
• Almost sure invariance principle for nonuniformly hyperbolic systems
• Slow rates of mixing for dynamical systems with hyperbolic structures
• Recent advances in invariance principles for stationary sequences
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• Distribution function inequalities for martingales
• Statistical properties of dynamical systems with some hyperbolicity
• Recurrence times and rates of mixing
• Multidimensional nonhyperbolic attractors
• Statistical limit theorems for suspension flows
• Dependent central limit theorems and invariance principles
• Central limit theorems for additive functionals of Markov chains.
• Sharp polynomial estimates for the decay of correlations
• Asymptotic theory of weakly dependent stochastic processes
• Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction
• Rate of convergence in the weak invariance principle for deterministic systems
• Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems
• Strong invariance principles with rate for ``reverse martingale differences and applications
• Deterministic homogenization for fast-slow systems with chaotic noise
• Moment bounds and concentration inequalities for slowly mixing dynamical systems
• Statistical properties of diffeomorphisms with weak invariant manifolds
• Markov structures and decay of correlations for non-uniformly expanding dynamical systems
• A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion
• Linear response for intermittent maps with summable and nonsummable decay of correlations
• Spatial structure of Sinai–Ruelle–Bowen measures
• Convergence of moments for Axiom A and non-uniformly hyperbolic flows
• Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems
• A note on diffusion limits of chaotic skew-product flows
• Positive Liapunov exponents and absolute continuity for maps of the interval
• Statistical properties of a skew product with a curve of neutral points
• Large deviations for nonuniformly hyperbolic systems
• The statistical stability of equilibrium states for interval maps
• Singular-hyperbolic attractors are chaotic
• Almost sure invariance principles for partial sums of weakly dependent random variables
• A probabilistic approach to intermittency
• Limit theorems for partially hyperbolic systems
• Statistical stability for robust classes of maps with non-uniform expansion
• Strong statistical stability of non-uniformly expanding maps
• SRB measures for non-hyperbolic systems with multidimensional expansion
• Billiards with polynomial mixing rates
• Homogenization for deterministic maps and multiplicative noise
• A FAMILY OF CHAOTIC BILLIARDS WITH VARIABLE MIXING RATES
• Sinai billiards under small external forces

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