Lyapunov Exponents Of Linear Cocycles: Continuity via Large Deviations by Pedro DuarteLyapunov Exponents Of Linear Cocycles: Continuity via Large Deviations by Pedro Duarte

Lyapunov Exponents Of Linear Cocycles: Continuity via Large Deviations

byPedro Duarte, Silvius Klein

Hardcover | March 30, 2016

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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.
Title:Lyapunov Exponents Of Linear Cocycles: Continuity via Large DeviationsFormat:HardcoverDimensions:263 pagesPublished:March 30, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9462391238

ISBN - 13:9789462391239

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Table of Contents

Introduction.- Estimates on Grassmann Manifolds.- Abstract Continuity of Lyapunov Exponents.- The Oseledets Filtration and Decomposition.- Large Deviations for Random Cocycles.- Large Deviations for Quasi-Periodic Cocycles.- Further Related Problems.