Dimension and Recurrence in Hyperbolic Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dimension and Recurrence in Hyperbolic Dynamics write by Luis Barreira. This book was released on 2009-08-29. Dimension and Recurrence in Hyperbolic Dynamics available in PDF, EPUB and Kindle. 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.
Dimension and Recurrence in Hyperbolic Dynamics
Dimension and Recurrence in Hyperbolic Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dimension and Recurrence in Hyperbolic Dynamics write by Luis Barreira. This book was released on 2008-11-05. Dimension and Recurrence in Hyperbolic Dynamics available in PDF, EPUB and Kindle. 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, Hyperbolic Dynamics and Dimension Theory
Ergodic Theory, Hyperbolic Dynamics and Dimension Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ergodic Theory, Hyperbolic Dynamics and Dimension Theory write by Luís Barreira. This book was released on 2012-04-28. Ergodic Theory, Hyperbolic Dynamics and Dimension Theory available in PDF, EPUB and Kindle. 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
Dimension Theory of Hyperbolic Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dimension Theory of Hyperbolic Flows write by Luís Barreira. This book was released on 2013-06-12. Dimension Theory of Hyperbolic Flows available in PDF, EPUB and Kindle. 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.
Dynamics Beyond Uniform Hyperbolicity
Dynamics Beyond Uniform Hyperbolicity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamics Beyond Uniform Hyperbolicity write by Christian Bonatti. This book was released on 2006-03-30. Dynamics Beyond Uniform Hyperbolicity available in PDF, EPUB and Kindle. What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n
