[图书][B] Extremes and recurrence in dynamical systems
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems
presents a unique point of view on the mathematical theory of extremes and on its …
presents a unique point of view on the mathematical theory of extremes and on its …
[PS][PS] Inequalities for the occurrence times of rare events in mixing processes. The state of the art
The rst occurrence time of a rare event in a mixing process typically has a distribution which
can be well approximated by the exponential law. In this paper we review recent theorems …
can be well approximated by the exponential law. In this paper we review recent theorems …
Statistics of Return Times:¶ A General Framework and New Applications
In this paper we provide general estimates for the errors between the distribution of the first,
and more generally, the K th return time (suitably rescaled) and the Poisson law for …
and more generally, the K th return time (suitably rescaled) and the Poisson law for …
Hitting and return times in ergodic dynamical systems
Given an ergodic dynamical system (X, T, μ), and U⊂ X measurable with μ (U)> 0, let μ (U) τ
U (x) denote the normalized hitting time of x∈ X to U. We prove that given a sequence (U n) …
U (x) denote the normalized hitting time of x∈ X to U. We prove that given a sequence (U n) …
[PDF][PDF] Inequalities for hitting times in mixing dynamical systems
A Galves, B Schmitt - Random and Computational Dynamics, 1997 - researchgate.net
We prove that a hitting time of a mixing dynamical system can be sharply approximated by
an exponential random variable. More precisely, we prove that there exists four strictly …
an exponential random variable. More precisely, we prove that there exists four strictly …
Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems
JR Chazottes, P Collet - Ergodic Theory and Dynamical Systems, 2013 - cambridge.org
We study the number of visits to balls Br (x), up to time t/μ (Br (x)), for a class of non-uniformly
hyperbolic dynamical systems, where μ is the Sinai–Ruelle–Bowen measure. Outside a set …
hyperbolic dynamical systems, where μ is the Sinai–Ruelle–Bowen measure. Outside a set …
Mixing limit theorems for ergodic transformations
R Zweimüller - Journal of Theoretical Probability, 2007 - Springer
We show that distributional and weak functional limit theorems for ergodic processes often
hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the …
hold for arbitrary absolutely continuous initial distributions. This principle is illustrated in the …
[图书][B] Concepts and results in chaotic dynamics: a short course
P Collet, JP Eckmann - 2006 - books.google.com
This book is devoted to the subject commonly called Chaotic Dynamics, namely the study of
complicated behavior in time of maps and? ows, called dynamical systems. The theory of …
complicated behavior in time of maps and? ows, called dynamical systems. The theory of …
[HTML][HTML] Rare events for the Manneville–Pomeau map
We prove a dichotomy for Manneville–Pomeau maps f:[0, 1]→[0, 1]: given any point ζ∈[0, 1],
either the Rare Events Point Processes (REPP), counting the number of exceedances …
either the Rare Events Point Processes (REPP), counting the number of exceedances …
Dispersing billiards with cusps: slow decay of correlations
N Chernov, R Markarian - Communications in mathematical physics, 2007 - Springer
Dispersing billiards introduced by Sinai are uniformly hyperbolic and have strong statistical
properties (exponential decay of correlations and various limit theorems). However, if the …
properties (exponential decay of correlations and various limit theorems). However, if the …