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# π Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations by Pedro Duarte, Silvius Klein (auth.) β epub download

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The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.

- Series:
**Atlantis Studies in Dynamical Systems 3** - Author:
**Pedro Duarte, Silvius Klein (auth.)** - Year:
**2016** - Publisher:
**Atlantis Press** - Language:
**English** - ISBN:
**978-94-6239-123-9, 978-94-6239-124-6**

- File size:
**3 119 559** - Format:
**pdf**

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Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.Specifically, a linear differential system is considered which is controlled by a stochas...

Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.Specifically, a linear differential system is considered which is controlled by a stochas...

Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in partic...

Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, prono...

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is a time-continu...

Applies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysisβa consistent new approach The theory of large deviations, one of the most dynamic topics in probability today, studies rare events...

This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute cont...

The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that a...

This book presents an introduction to the theory of large deviations. Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. The mathematics...