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Almost Sure Invariance Principle for Nonuniformly Hyperbolic Systems
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered byExpand
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A vector-valued almost sure invariance principle for hyperbolic dynamical systems
We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. TheseExpand
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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 areaExpand
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Large deviations for nonuniformly hyperbolic systems
We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decayExpand
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Acceleration of one-dimensional mixing by discontinuous mappings
The paper considers a simple class of models for mixing of a passive tracer into a bulk material that is essentially one dimensional. We examine the relative rates of mixing due to diffusion, stretchExpand
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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 ofExpand
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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 withExpand
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Symmetry of attractors and the Karhunen-Loegve decomposition
Recent fluid dynamics experiments [13, 10, 4] have shown that the symmetry of attractors can manifest itself through the existence of spatially regular patterns in the time average of an appropriateExpand
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A Borel-Cantelli lemma for nonuniformly expanding dynamical systems
Let be a sequence of sets in a probability space such that . The classical Borel–Cantelli (BC) lemma states that if the sets An are independent, then μ({x X : x An for infinitely many values of n}) =Expand
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Almost sure invariance principle for sequential and non-stationary dynamical systems
We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples includeExpand
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