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A probabilistic approach to intermittency
TLDR
This method essentially gives the optimal polynomial bound for the decay of correlations, the degree depending on the order of the tangency at the neutral fixed point.
Extremes and Recurrence in Dynamical Systems
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area
Statistics of Return Times:¶A General Framework and New Applications
Abstract:In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the Kth return time (suitably rescaled) and the Poisson law for
Polynomial loss of memory for maps of the interval with a neutral fixed point
We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of
Annealed and quenched limit theorems for random expanding dynamical systems
In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with
A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems
We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance
Recurrence, Dimensions, and Lyapunov Exponents
We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.
Almost sure invariance principle for random piecewise expanding maps
We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques.
Laws of rare events for deterministic and random dynamical systems
The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non
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