Duarte, Pedro. <br/><br/>
Lyapunov Exponents of Linear Cocycles  Continuity via Large Deviations /  [electronic resource] : 
by Pedro Duarte, Silvius Klein. 
 - 1st ed. 2016. 
 - XIII, 263 p. 4 illus.  online resource. 
 - Atlantis Studies in Dynamical Systems ;  3 .
 - Atlantis Studies in Dynamical Systems ;  3 .
<br/><br/>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. 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9789462391246 
<br/><br/><label>Standard No.: </label>10.2991/978-94-6239-124-6  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematics.<br/>Dynamics.<br/>Ergodic theory.<br/>Mathematical physics.<br/>Mathematics.<br/>Dynamical Systems and Ergodic Theory.<br/>Mathematical Physics.
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Electronic books.
<br/><br/><label>LC Class. No.: </label>QA313 
<br/><br/><label>Dewey Class. No.: </label>515.39 515.48