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Lyapunov Exponents of Linear Cocycles : Continuity via Large Deviations / by Pedro Duarte, Silvius Klein.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Duarte, Pedro, Author.
- Klein, Silvius., Author.
- Series:
- Atlantis Studies in Dynamical Systems, 2213-3534 ; 3
- Language:
- English
- Subjects (All):
- Dynamics.
- Mathematical physics.
- Dynamical Systems.
- Mathematical Physics.
- Local Subjects:
- Dynamical Systems.
- Mathematical Physics.
- Physical Description:
- 1 online resource (271 p.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Paris : Atlantis Press : Imprint: Atlantis Press, 2016.
- Language Note:
- English
- 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 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.
- 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.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references at the end of each chapters and index.
- ISBN:
- 94-6239-124-6
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