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Description
This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.
Table of Contents
Introduction.- Part I - Basic Theory.- Lyapunov Exponents and Regularity.- Sequences of Matrices.- Linear Differential Equations.- Part II - Further Topics.- Singular Values.- Characterizations of Regularity.- Part III - Hyperbolicity and Ergodic Theory.- Tempered Dichotomies.- Lyapunov Sequences.- Cocycles and Lyapunov Exponents.- Lyapunov Functions and Cones.- Part IV - Multifractal Analysis.- Entropy Spectrum.- Accumulation Sets.
