Lyapunov Exponents of Linear Cocycles
Continuity via Large Deviations
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Beschreibung
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.
Unified approach to proving continuity of Lyapunov exponents for various types of linear cocycles Uniform large deviation type estimates established for iterates of general quasi-periodic and random cocycles A general Avalanche Principle for compositions of linear maps derived using a geometric approach A list of related open problems Includes supplementary material: sn.pub/extras
Autor*in
Pedro Duarte
Themen in »Lyapunov Exponents of Linear Cocycles«
Bernoulli Cocycles Large Deviations Lyapunov Exponents Quasi-periodic Cocycles Subharmonic Functions
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“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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