Nonuniform Hyperbolicity PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Nonuniform Hyperbolicity PDF full book. Access full book title Nonuniform Hyperbolicity.
| Author | : José F. Alves |
| Publisher | : Springer Nature |
| Total Pages | : 259 |
| Release | : 2020-12-19 |
| Genre | : Mathematics |
| ISBN | : 3030628140 |
Download Nonuniformly Hyperbolic Attractors Book in PDF, ePub and Kindle
This monograph offers a coherent, self-contained account of the theory of Sinai–Ruelle–Bowen measures and decay of correlations for nonuniformly hyperbolic dynamical systems. A central topic in the statistical theory of dynamical systems, the book in particular provides a detailed exposition of the theory developed by L.-S. Young for systems admitting induced maps with certain analytic and geometric properties. After a brief introduction and preliminary results, Chapters 3, 4, 6 and 7 provide essentially the same pattern of results in increasingly interesting and complicated settings. Each chapter builds on the previous one, apart from Chapter 5 which presents a general abstract framework to bridge the more classical expanding and hyperbolic systems explored in Chapters 3 and 4 with the nonuniformly expanding and partially hyperbolic systems described in Chapters 6 and 7. Throughout the book, the theory is illustrated with applications. A clear and detailed account of topics of current research interest, this monograph will be of interest to researchers in dynamical systems and ergodic theory. In particular, beginning researchers and graduate students will appreciate the accessible, self-contained presentation.
| Author | : L.A. Bunimovich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 476 |
| Release | : 2000-04-05 |
| Genre | : Mathematics |
| ISBN | : 9783540663164 |
Download Dynamical Systems, Ergodic Theory and Applications Book in PDF, ePub and Kindle
This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.
| Author | : Luis Barreira |
| Publisher | : |
| Total Pages | : |
| Release | : 2014-02-19 |
| Genre | : |
| ISBN | : 9781299707306 |
Download Nonuniform Hyperbolicity Book in PDF, ePub and Kindle
A self-contained, comprehensive account of modern smooth ergodic theory, the mathematical foundation of deterministic chaos.
| Author | : Luís Barreira |
| Publisher | : Springer |
| Total Pages | : 145 |
| Release | : 2018-05-02 |
| Genre | : Mathematics |
| ISBN | : 3319901109 |
Download Admissibility and Hyperbolicity Book in PDF, ePub and Kindle
This book gives a comprehensive overview of the relationship between admissibility and hyperbolicity. Essential theories and selected developments are discussed with highlights to applications. The dedicated readership includes researchers and graduate students specializing in differential equations and dynamical systems (with emphasis on hyperbolicity) who wish to have a broad view of the topic and working knowledge of its techniques. The book may also be used as a basis for appropriate graduate courses on hyperbolicity; the pointers and references given to further research will be particularly useful. The material is divided into three parts: the core of the theory, recent developments, and applications. The first part pragmatically covers the relation between admissibility and hyperbolicity, starting with the simpler case of exponential contractions. It also considers exponential dichotomies, both for discrete and continuous time, and establishes corresponding results building on the arguments for exponential contractions. The second part considers various extensions of the former results, including a general approach to the construction of admissible spaces and the study of nonuniform exponential behavior. Applications of the theory to the robustness of an exponential dichotomy, the characterization of hyperbolic sets in terms of admissibility, the relation between shadowing and structural stability, and the characterization of hyperbolicity in terms of Lyapunov sequences are given in the final part.
| Author | : A. Katok |
| Publisher | : Elsevier |
| Total Pages | : 1235 |
| Release | : 2005-12-17 |
| Genre | : Mathematics |
| ISBN | : 0080478220 |
Download Handbook of Dynamical Systems Book in PDF, ePub and Kindle
This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey “Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations). . Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
| Author | : Luis Barreira |
| Publisher | : World Scientific |
| Total Pages | : 241 |
| Release | : 2021-03-12 |
| Genre | : Mathematics |
| ISBN | : 9811230269 |
Download Hyperbolicity In Delay Equations Book in PDF, ePub and Kindle
This book provides a comprehensive introduction to the study of hyperbolicity in both linear and nonlinear delay equations. This includes a self-contained discussion of the foundations, main results and essential techniques, with emphasis on important parts of the theory that apply to a large class of delay equations. The central theme is always hyperbolicity and only topics that are directly related to it are included. Among these are robustness, admissibility, invariant manifolds, and spectra, which play important roles in life sciences, engineering and control theory, especially in delayed feedback mechanisms.The book is dedicated to researchers as well as graduate students specializing in differential equations and dynamical systems who wish to have an extensive and in-depth view of the hyperbolicity theory of delay equations. It can also be used as a basis for graduate courses on the stability and hyperbolicity of delay equations.
| Author | : Luis Barreira |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 302 |
| Release | : 2008-11-05 |
| Genre | : Mathematics |
| ISBN | : 376438882X |
Download Dimension and Recurrence in Hyperbolic Dynamics Book 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.
| Author | : Robert A. Meyers |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1885 |
| Release | : 2011-10-05 |
| Genre | : Mathematics |
| ISBN | : 1461418054 |
Download Mathematics of Complexity and Dynamical Systems Book in PDF, ePub and Kindle
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
| Author | : Luís Barreira |
| Publisher | : American Mathematical Society |
| Total Pages | : 355 |
| Release | : 2023-04-28 |
| Genre | : Mathematics |
| ISBN | : 1470473070 |
Download Introduction to Smooth Ergodic Theory Book in PDF, ePub and Kindle
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.
| Author | : Jack K. Hale |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 286 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387228969 |
Download Dynamics in Infinite Dimensions Book in PDF, ePub and Kindle
State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications
