Poisson law for some non-uniformly hyperbolic dynamical systems with polynomial rate of mixing
From MaRDI portal
Publication:2976310
DOI10.1017/etds.2015.28zbMath1362.37074arXiv1401.3599OpenAlexW2963982938MaRDI QIDQ2976310
Françoise Pène, Benoît Saussol
Publication date: 28 April 2017
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1401.3599
Ergodicity, mixing, rates of mixing (37A25) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Convergence of probability measures (60B10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)
Related Items (21)
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 ⋮ Extreme value laws for dynamical systems with countable extremal sets ⋮ Maximal large deviations and slow recurrences in weakly chaotic systems ⋮ Hitting times and positions in rare events ⋮ Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems ⋮ Poisson limit distribution for diffeomorphisms with weak hyperbolic product structure ⋮ Cluster distributions for dynamically defined point processes ⋮ Spatio-temporal Poisson processes for visits to small sets ⋮ 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 ⋮ Rare event process and entry times distribution for arbitrary null sets on compact manifolds ⋮ Geometric law for numbers of returns until a hazard under \(\varphi\)-mixing ⋮ A Poisson limit theorem for Gibbs–Markov maps ⋮ 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 ⋮ Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems
Cites Work
- Limit theorems in the stadium billiard
- Slow rates of mixing for dynamical systems with hyperbolic structures
- Statistical properties of dynamical systems with some hyperbolicity
- Recurrence times and rates of mixing
- Dimension and product structure of hyperbolic measures
- Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains
- Recurrence rate in rapidly mixing dynamical systems
- Convergence of rare event point processes to the Poisson process for planar billiards
- Poincaré recurrence for observations
- A probabilistic approach to intermittency
- Billiards with polynomial decay of correlations
- Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems
- Billiards with polynomial mixing rates
- Hausdorff dimension of measures via Poincaré recurrence
This page was built for publication: Poisson law for some non-uniformly hyperbolic dynamical systems with polynomial rate of mixing
