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Dimension Theory of Hyperbolic Flows (Springer Monographs in Mathematics)

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en Limba Engleză Carte Paperback – 10 Jul 2015
The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs.
 
The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.
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Specificații

ISBN-13: 9783319033921
ISBN-10: 3319033921
Pagini: 168
Dimensiuni: 155 x 235 x 9 mm
Greutate: 0.25 kg
Ediția: 2013
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării: Cham, Switzerland

Public țintă

Research

Cuprins

1.Introduction.- Part I Basic Notions.- 2.Suspension Flows.- 3.Hyperbolic Flows.- 4.Pressure and Dimension.- Part II Dimension Theory.- 5.Dimension of Hyperbolic Sets.- 6.Pointwise Dimension and Applications.- Part III Multifractal Analysis.- 7.Suspensions over Symbolic Dynamics.- 8.Multifractal Analysis of Hyperbolic Flows.- Part IV Variational Principles.- 9.Entropy Spectra.- 10.Multidimensional Spectra.- 11.Dimension Spectra.- References.- Index.

Notă biografică

Luis Barreira is a Professor of Mathematics at the Instituto Superior Técnico in Lisbon. He is the author of 17 books, including several textbooks published in several languages, and more than 100 articles on mathematics, mainly on differential equations, dynamical systems and ergodic theory.

Textul de pe ultima copertă

The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs.
 
The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.

Caracteristici

First comprehensive exposition of dimension theory of hyperbolic flows
 
Includes an overview of dimension theory and multifractal analysis
 
Includes a detailed discussion of major open problems in the area