Extremes and extremal indices for level set observables on hyperbolic systems *

DOI10.1088/1361-6544/ABD85FzbMath1464.37005arXiv1909.04748OpenAlexW3132777629MaRDI QIDQ5854634

M. P. Holland, Meagan Carney, Matthew Nicol

Publication date: 17 March 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.04748

zbMATH Keywords

stationary stochastic processesmetastabilityextreme value theoryreturn-time statistics

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Extreme value theory; extremal stochastic processes (60G70) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (5)

Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Mean-field coupled systems and self-consistent transfer operators: a review ⋮ Cluster distributions for dynamically defined point processes ⋮ Rare event process and entry times distribution for arbitrary null sets on compact manifolds ⋮ Escape rate and conditional escape rate from a probabilistic point of view

Uses Software

• ismev

Cites Work

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• Likelihood estimation of the extremal index
• Almost sure convergence of maxima for chaotic dynamical systems
• Extreme value laws in dynamical systems for non-smooth observations
• The extremal index, hitting time statistics and periodicity
• Dispersing billiards with cusps: slow decay of correlations
• On the link between dependence and independence in extreme value theory for dynamical systems
• Hitting time statistics and extreme value theory
• Back to balls in billiards
• Extremes and related properties of random sequences and processes
• Statistical properties of dynamical systems with some hyperbolicity
• A Poisson limit theorem for toral automorphisms
• Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems
• Towards a general theory of extremes for observables of chaotic dynamical systems
• Speed of convergence for laws of rare events and escape rates
• The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
• Extreme value laws in dynamical systems under physical observables
• Statistics of closest return for some non-uniformly hyperbolic systems
• Extremes and Recurrence in Dynamical Systems
• Quantitative recurrence statistics and convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems
• Extreme value statistics for dynamical systems with noise
• Convergence of rare event point processes to the Poisson process for planar billiards
• Rare events, exponential hitting times and extremal indices via spectral perturbation†
• Escape rates for Gibbs measures
• Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps
• Extreme value theory for non-uniformly expanding dynamical systems
• Statistical properties of two-dimensional hyperbolic billiards
• Extreme value theory for synchronization of coupled map lattices
• Extremal dichotomy for uniformly hyperbolic systems
• Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems
• Poisson law for Axiom A diffeomorphisms
• ANALYSIS OF ROUND OFF ERRORS WITH REVERSIBILITY TEST AS A DYNAMICAL INDICATOR
• Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems
• Markov partitions for two-dimensional hyperbolic billiards
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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