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Lyapunov exponents of linear cocycles : continuity via large deviations

Author: Pedro Duarte; Silvius Klein
Publisher: [Place of publication not identified] : Atlantis Press, 2016.
Series: Atlantis series in dynamical systems, v. 3.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)907193351
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Pedro Duarte; Silvius Klein
ISBN: 9789462391246 9462391246
OCLC Number: 945445122
Description: 1 online resource.
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.
Series Title: Atlantis series in dynamical systems, v. 3.
Responsibility: Pedro Duarte, Silvius Klein.
More information:

Abstract:

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.

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