Springer International Publishing AG, 2017. – 273 p. – ISBN 3319712608. This book is a self-contained introduction to the theory of Lyapunov exponents and its applications, particularly in connection with hyperbolicity, ergodic theory, and multifractal analysis. It includes the discussion of the foundations and of some of the main results and main techniques in the area. It also gives a panorama of selected topics of current research interest. I emphasize that unlike in most other works, Lyapunov exponents are from beginning to end the main theme, of course with many variations and with nontrivial connections to other areas. Contents Introduction Basic Theory Lyapunov Exponents and Regularity Sequences of Matrices Linear Differential Equations Lyapunov–Perron Regularity Further Topics Preservation of Lyapunov Exponents Singular Values Characterizations of Regularity Regularity and Adjoint Sequences Hyperbolicity and Ergodic Theory Tempered Dichotomies Lyapunov Sequences Cocycles and Lyapunov Exponents . Lyapunov Functions and Cones Multifractal Analysis Entropy Spectrum Accumulation Sets
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