Lyapunov Exponents

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. Front Matter ....Pages i-xi Introduction (Luís Barreira)....Pages 1-28 Front Matter ....Pages 29-29 Lyapunov Exponents and Regularity (Luís Barreira)....Pages 31-41 Sequences of Matrices (Luís Barreira)....Pages 43-69 Linear Differential Equations (Luís Barreira)....Pages 71-88 Front Matter ....Pages 89-89 Preservation of Lyapunov Exponents (Luís Barreira)....Pages 91-113 Singular Values (Luís Barreira)....Pages 115-135 Characterizations of Regularity (Luís Barreira)....Pages 137-165 Front Matter ....Pages 167-167 Tempered Dichotomies (Luís Barreira)....Pages 169-186 Lyapunov Sequences (Luís Barreira)....Pages 187-202 Cocycles and Lyapunov Exponents (Luís Barreira)....Pages 203-222 Lyapunov Functions and Cones (Luís Barreira)....Pages 223-236 Front Matter ....Pages 237-237 Entropy Spectrum (Luís Barreira)....Pages 239-252 Accumulation Sets (Luís Barreira)....Pages 253-264 Back Matter ....Pages 265-273