Extremal dichotomy for uniformly hyperbolic systems

DOI10.1080/14689367.2015.1056722zbMath1357.37009arXiv1501.05023OpenAlexW1720497802MaRDI QIDQ3462333

Jorge Milhazes Freitas, M. P. Holland, Ana Cristina Moreira Freitas, Maria Pires De Carvalho, Matthew Nicol

Publication date: 5 January 2016

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.05023

zbMATH Keywords

stationary stochastic processespoint processesextreme value theoryextremal indexreturn 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) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (9)

Almost sure convergence of maxima for chaotic dynamical systems ⋮ Multiple Borel-Cantelli lemma in dynamics and multilog law for recurrence ⋮ Compound Poisson law for hitting times to periodic orbits in two-dimensional hyperbolic systems ⋮ Cluster distributions for dynamically defined point processes ⋮ Extreme value distributions of observation recurrences ⋮ Complete convergence and records for dynamically generated stochastic processes ⋮ On the computation of the extremal index for time series ⋮ Matching of observations of dynamical systems, with applications to sequence matching ⋮ Extremes and extremal indices for level set observables on hyperbolic systems ^*

Cites Work

• Rare events for the Manneville-Pomeau map
• The extremal index, hitting time statistics and periodicity
• On the link between dependence and independence in extreme value theory for dynamical systems
• Hitting time statistics and extreme value theory
• Speed of convergence for laws of rare events and escape rates
• The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics
• The compound Poisson distribution and return times in dynamical systems
• Statistics of closest return for some non-uniformly hyperbolic systems
• 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
• Laws of rare events for deterministic and random dynamical systems
• 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
• Speed of convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems
• Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems
• Limit theorems for partially hyperbolic systems
• Poisson law for Axiom A diffeomorphisms
• Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems
• There are No New Anosov Diffeomorphisms on Tori
• On extreme values in stationary sequences
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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