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Lyapunov exponents of linear cocycle...

Duarte, Pedro.

Lyapunov exponents of linear cocyclescontinuity via large deviations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lyapunov exponents of linear cocyclesby Pedro Duarte, Silvius Klein.
Reminder of title:	continuity via large deviations /
Author:	Duarte, Pedro.
other author:	Klein, Silvius.
Published:	Paris :Atlantis Press :2016.
Description:	xiii, 263 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Lyapunov exponents.
Online resource:	http://dx.doi.org/10.2991/978-94-6239-124-6
ISBN:	9789462391246$q(electronic bk.)

Lyapunov exponents of linear cocyclescontinuity via large deviations /
Duarte, Pedro.

Lyapunov exponents of linear cocyclescontinuity via large deviations /[electronic resource] :by Pedro Duarte, Silvius Klein. - Paris :Atlantis Press :2016. - xiii, 263 p. :ill., digital ;24 cm. - Atlantis studies in dynamical systems ;v.3. - Atlantis studies in dynamical systems ;v.1..

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.

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.

ISBN: 9789462391246$q(electronic bk.)

Standard No.: 10.2991/978-94-6239-124-6doiSubjects--Topical Terms:

742215
Lyapunov exponents.

LC Class. No.: QA372

Dewey Class. No.: 515.35

Lyapunov exponents of linear cocyclescontinuity via large deviations /
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245 1 0 $a Lyapunov exponents of linear cocycles $h [electronic resource] : $b continuity via large deviations / $c by Pedro Duarte, Silvius Klein.
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490 1 $a Atlantis studies in dynamical systems ; $v v.3
505 0 $a 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.
520 $a 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.
650 0 $a Lyapunov exponents. $3 742215
650 0 $a Cocycles. $3 742216
650 0 $a Grassmann manifolds. $3 709163
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Mathematical Physics. $3 522725
700 1 $a Klein, Silvius. $3 742214
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950 $a Mathematics and Statistics (Springer-11649)