Lyapunov Exponents of Linear Cocycles
Continuity via Large Deviations
(Sprache: Englisch)
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...
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Klappentext zu „Lyapunov Exponents of Linear Cocycles “
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.
Inhaltsverzeichnis zu „Lyapunov Exponents of Linear Cocycles “
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.
Bibliographische Angaben
- Autoren: Pedro Duarte , Silvius Klein
- 2016, 1st ed. 2016, XIII, 263 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 9462391238
- ISBN-13: 9789462391239
- Erscheinungsdatum: 30.03.2016
Sprache:
Englisch
Pressezitat
"The effort of the authors to make this text self-contained and to make the exposition very clear and delightful was successful, making this monograph an excellent contribution for both graduate student and anyone interested in the continuity of Lyapunov Exponents." (Paulo Varandas, Mathematical Reviews, June, 2018)
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