Lyapunov Exponents - Luís Barreira

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Résumé :
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. ...

Biographie:
Lu?s Barreira is a professor of Mathematics at Universidade de Lisboa - Instituto Superior T?cnico, Portugal with a long experience in teaching and research. PhD in Mathematics from Penn State University, 1996. Received the Gulbenkian Science prize in 2007, the UTL/Santander Totta Mathematics prize in 2007, the Ferran Sunyer i Balaguer prize in 2008 (with the book Dimension and Recurrence in Hyperbolic Dynamics, Birkh?user), and the UL/CGD Mathematics prize, 2023. Author or co-author of several books published by the AMS, Birkh?user, Cambridge University Press, Springer, and World Scientific, at various levels (those in English include 8 research monographs and 7 textbooks). Author or co-author of many articles in mathematics, mainly in the areas differential equations and dynamical systems, and mostly in ergodic theory and hyperbolicity theory. Claudia Valls is a professor of Mathematics at Universidade de Lisboa - Instituto Superior T?cnico,Portugal, with a long experience in teaching and research. PhD in Mathematics from Universitat de Barcelona, 1999. She received the UTL/Santander Totta Mathematics prize in 2008. She is the co-author of 8 books in English published by the AMS, Springer, and World Scientific (include 3 research monographs and 5 textbooks). Author or co-author of many articles in mathematics, mainly in differential equations and dynamical systems, and mostly in integrability theory and hyperbolicity theory....

Sommaire:
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. ...