Lyapunov Exponents of Linear Cocycles Continuity Via Large Deviations |
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| Author:
| Duarte, Pedro
Klein, Silvius |
| Series title: | Atlantis Studies in Dynamical Systems Ser. |
| ISBN: | 978-94-6239-123-9 |
| Publication Date: | Mar 2016 |
| Publisher: | Atlantis Press (Zeger Karssen)
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| Book Format: | Hardback |
| List Price: | USD $109.00USD $109.00 |
Book Description:
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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...
More DescriptionThe 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.