Lyapunov Exponents of Linear Cocycles

Continuity via Large Deviations

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Science, Physics, Mathematical Physics
Cover of the book Lyapunov Exponents of Linear Cocycles by Pedro Duarte, Silvius Klein, Atlantis Press
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Author: Pedro Duarte, Silvius Klein ISBN: 9789462391246
Publisher: Atlantis Press Publication: March 21, 2016
Imprint: Atlantis Press Language: English
Author: Pedro Duarte, Silvius Klein
ISBN: 9789462391246
Publisher: Atlantis Press
Publication: March 21, 2016
Imprint: Atlantis Press
Language: English

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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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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