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Lyapunov Exponents de Luís Barreira

Lyapunov Exponents

Autor Luís Barreira
en Limba Engleză Hardback – 30 ian 2018
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. 
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Specificații

ISBN-13: 9783319712604
ISBN-10: 3319712608
Pagini: 288
Ilustrații: XI, 273 p.
Dimensiuni: 160 x 241 x 22 mm
Greutate: 0.6 kg
Ediția:1st edition 2017
Editura: birkhäuser
Locul publicării:Cham, Switzerland

Cuprins

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.

Recenzii

“This monograph is a good source on the theory of Lyapunov exponents and their applications to fields as ergodic theory, hyperbolic dynamical systems, and multifractal analysis. The book is self-contained and is addressed to researchers of dynamical systems theory, as well as to all interested mathematicians from related fields. … The book contains an extensive bibliography.” (Ivan Podvigin, zbMATH 1407.37001, 2019)

“The book gives a good introduction to and an overview of the recent results on the abstract theory of Lyapunov exponents, with a focus on regularity theory. … This book can be read and understood by a novice, while it comprises an overview of some very recent results useful for an expert. It complements well the 'existing literature on Lyapunov exponents, notably on a now-classical theory of nonuniform hyperbolicity and Pesin theory … .” (Sinisa Slijepcevic, Mathematical Reviews, December, 2018)

Textul de pe ultima copertă

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.

Caracteristici

Lyapunov exponents are the main theme from beginning to end
Provides a comprehensive overview of the theory’s foundations
Highlights selected topics of current research interest

Notă biografică

Luís Barreira is a professor of Mathematics at Universidade de Lisboa - Instituto Superior Técnico, 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, Birkhäuser), and the UL/CGD Mathematics prize, 2023. Author or co-author of several books published by the AMS, Birkhäuser, 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 Técnico,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.