Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

2012-04-28 Mathematics

Author : Luís Barreira
Release : 2012-04-28
Genre : Mathematics
Kind : eBook
Book Rating : 900/5 ( reviews)

GET EBOOK

Book Synopsis Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by : Luís Barreira

Download or read book Ergodic Theory, Hyperbolic Dynamics and Dimension Theory written by Luís Barreira. This book was released on 2012-04-28. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

2012-05-06 Mathematics

Author : Luis Barreira
Release : 2012-05-06
Genre : Mathematics
Kind : eBook
Book Rating : 917/5 ( reviews)

GET EBOOK

Book Synopsis Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by : Luis Barreira

Download or read book Ergodic Theory, Hyperbolic Dynamics and Dimension Theory written by Luis Barreira. This book was released on 2012-05-06. Available in PDF, EPUB and Kindle. Book excerpt: Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Dimension Theory of Hyperbolic Flows

2013-06-12 Mathematics

Author : Luís Barreira
Release : 2013-06-12
Genre : Mathematics
Kind : eBook
Book Rating : 480/5 ( reviews)

GET EBOOK

Book Synopsis Dimension Theory of Hyperbolic Flows by : Luís Barreira

Download or read book Dimension Theory of Hyperbolic Flows written by Luís Barreira. This book was released on 2013-06-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dimension and Recurrence in Hyperbolic Dynamics

2008-11-05 Mathematics

Author : Luis Barreira
Release : 2008-11-05
Genre : Mathematics
Kind : eBook
Book Rating : 82X/5 ( reviews)

GET EBOOK

Book Synopsis Dimension and Recurrence in Hyperbolic Dynamics by : Luis Barreira

Download or read book Dimension and Recurrence in Hyperbolic Dynamics written by Luis Barreira. This book was released on 2008-11-05. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. This includes topics on irregular sets, var- tional principles, applications to number theory, measures of maximal dimension, multifractal rigidity, and quantitative recurrence. The book isdirected to researchersas well as graduate students whowish to have a global view of the theory together with a working knowledgeof its main techniques. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics. I hope that the book may serve as a fast entry point to this exciting and active ?eld of research, and also that it may lead to further developments.

Ergodic Theory

2023-07-31 Mathematics

Author : Cesar E. Silva
Release : 2023-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)

GET EBOOK

Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva. This book was released on 2023-07-31. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Popular eBooks

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

Dimension Theory of Hyperbolic Flows

Dimension and Recurrence in Hyperbolic Dynamics

Ergodic Theory

You may also like...