Lyapunov Exponents of Linear Cocycles - Continuity via Large Deviations

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.

Table des matières

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.

Commentaire

"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)

Détails du produit

• Auteurs: Pedr Duarte, Pedro Duarte, Silvius Klein
• Edition: Springer, Berlin
• Langues: Anglais
• Format d'édition: Livre Relié
• Sortie: 01.01.2016
• EAN: 9789462391239
• ISBN: 978-94-62-39123-9
• Pages: 263
• Dimensions: 162 mm x 243 mm x 21 mm
• Poids: 532 g
• Illustrations: XIII, 263 p. 4 illus.
• Thèmes: Atlantis Press; Atlantis Studies in Dynamical Systems; Atlantis Press; Atlantis Studies in Dynamical Systems
• Catégorie: Sciences naturelles, médecine, informatique, technique > Mathématiques > Analyse