Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

DOI10.3934/DCDS.2016.36.2585zbMath1341.37016arXiv1402.2990OpenAlexW2963033653MaRDI QIDQ256223

Nicolai T. A. Haydn, Kasia Wasilewska

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2990

zbMATH Keywords

attractorscorrelationspolynomial decayreturn times distribution

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (19)

Entry times distribution for mixing systems ⋮ Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Entry times distribution for dynamical balls on metric spaces ⋮ Measures, annuli and dimensions ⋮ Poisson limit distribution for diffeomorphisms with weak hyperbolic product structure ⋮ Cluster distributions for dynamically defined point processes ⋮ On the shortest distance between orbits and the longest common substring problem ⋮ Spatio-temporal Poisson processes for visits to small sets ⋮ Exponential law for random maps on compact manifolds* ⋮ Thin annuli property and exponential distribution of return times for weakly Markov systems ⋮ Hitting times distribution and extreme value laws for semi-flows ⋮ A derivation of the Poisson law for returns of smooth maps with certain geometrical properties ⋮ Complete convergence and records for dynamically generated stochastic processes ⋮ Limit theorems for numbers of returns in arrays under ϕ-mixing ⋮ Rare event process and entry times distribution for arbitrary null sets on compact manifolds ⋮ Local escape rates for -mixing dynamical systems ⋮ Limiting entry and return times distribution for arbitrary null sets ⋮ Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets ⋮ Poisson approximations and convergence rates for hyperbolic dynamical systems

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