A derivation of the Poisson law for returns of smooth maps with certain geometrical properties

DOI10.1090/conm/698/14031zbMath1398.37013OpenAlexW4256467184MaRDI QIDQ4686899

Fan Yang, Nicolai T. A. Haydn

Publication date: 10 October 2018

Published in: Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/698/14031

zbMATH Keywords

return times distributionextreme value lawinvariant measures of maps

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Ergodicity, mixing, rates of mixing (37A25) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (3)

Exponential law for random maps on compact manifolds* ⋮ Rare event process and entry times distribution for arbitrary null sets on compact manifolds ⋮ Limiting entry and return times distribution for arbitrary null sets

Cites Work

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• Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems
• Entry times distribution for mixing systems
• On the link between dependence and independence in extreme value theory for dynamical systems
• Extremes and related properties of random sequences and processes
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Dimension and product structure of hyperbolic measures
• A Poisson limit theorem for toral automorphisms
• Statistics of return times: A general framework and new applications
• Statistics of closest return for some non-uniformly hyperbolic systems
• Convergence of rare event point processes to the Poisson process for planar billiards
• Poisson law for some non-uniformly hyperbolic dynamical systems with polynomial rate of mixing
• Sharp errors for point-wise Poisson approximations in mixing processes
• Poisson limit law for Markov chains
• Return time statistics via inducing
• Limit theorems for partially hyperbolic systems
• Statistical properties of equilibrium states for rational maps
• Decay of correlations for piecewise smooth maps with indifferent fixed points
• Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems
• Return times distribution for Markov towers with decay of correlations
• Entry and return times distribution

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