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.
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 Luis Barreira. This book was released on 2013-06-30. Dimension Theory of Hyperbolic Flows available in PDF, EPUB and Kindle.
Three-Dimensional Flows
Three-Dimensional 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 Three-Dimensional Flows write by Vítor Araújo. This book was released on 2010-06-10. Three-Dimensional Flows available in PDF, EPUB and Kindle. In this book, the authors present the elements of a general theory for flows on three-dimensional compact boundaryless manifolds, encompassing flows with equilibria accumulated by regular orbits. The book aims to provide a global perspective of this theory and make it easier for the reader to digest the growing literature on this subject. This is not the first book on the subject of dynamical systems, but there are distinct aspects which together make this book unique. Firstly, this book treats mostly continuous time dynamical systems, instead of its discrete counterpart, exhaustively treated in some other texts. Secondly, this book treats all the subjects from a mathematical perspective with proofs of most of the results included. Thirdly, this book is meant to be an advanced graduate textbook and not just a reference book or monograph on the subject. This aspect is reflected in the way the cover material is presented, with careful and complete proofs, and precise references to topics in the book.
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 in Dynamical Systems
Dimension Theory in Dynamical Systems - 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 in Dynamical Systems write by Yakov B. Pesin. This book was released on 2008-04-15. Dimension Theory in Dynamical Systems available in PDF, EPUB and Kindle. The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
