Topological Dynamics And Applications
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Author |
: J. de Vries |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 762 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9789401581714 |
ISBN-13 |
: 9401581711 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Elements of Topological Dynamics by : J. de Vries
This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.
Author |
: Robert Ellis |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 348 |
Release |
: 1998 |
ISBN-10 |
: 9780821806081 |
ISBN-13 |
: 0821806084 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Topological Dynamics and Applications by : Robert Ellis
This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.
Author |
: |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 334 |
Release |
: 1998 |
ISBN-10 |
: 0821855514 |
ISBN-13 |
: 9780821855515 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Topological Dynamics and Applications by :
Author |
: Nguyen Dinh Cong |
Publisher |
: Oxford University Press |
Total Pages |
: 216 |
Release |
: 1997 |
ISBN-10 |
: 0198501579 |
ISBN-13 |
: 9780198501572 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Topological Dynamics of Random Dynamical Systems by : Nguyen Dinh Cong
This book is the first systematic treatment of the theory of topological dynamics of random dynamical systems. A relatively new field, the theory of random dynamical systems unites and develops the classical deterministic theory of dynamical systems and probability theory, finding numerous applications in disciplines ranging from physics and biology to engineering, finance and economics. This book presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.
Author |
: Michael Brin |
Publisher |
: Cambridge University Press |
Total Pages |
: 490 |
Release |
: 2004-08-16 |
ISBN-10 |
: 0521840732 |
ISBN-13 |
: 9780521840736 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Modern Dynamical Systems and Applications by : Michael Brin
This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.
Author |
: Robert Ellis |
Publisher |
: |
Total Pages |
: 240 |
Release |
: 1969 |
ISBN-10 |
: UCAL:B4406912 |
ISBN-13 |
: |
Rating |
: 4/5 (12 Downloads) |
Synopsis Lectures on Topological Dynamics by : Robert Ellis
Author |
: Konstantin Sergeevich Sibirskii |
Publisher |
: Springer |
Total Pages |
: 180 |
Release |
: 1975 |
ISBN-10 |
: UOM:39015015616710 |
ISBN-13 |
: |
Rating |
: 4/5 (10 Downloads) |
Synopsis Introduction to Topological Dynamics by : Konstantin Sergeevich Sibirskii
The theory of differential equations originated at the end of the seventeenth century in the works of I. Newton, G. W. Leibniz and others. During the first century of its existence, this theory consisted only of isolated methods of solving certain types of differential equations; but the problem of the existence of a solution and its representability in quadratures was posed already in the second. As a result of numerous investigations it became clear that integrability in quadratures is an extremely rare phe nomenon and that the solution of many differential equations arising in applications cannot be expressed in quadratures. Also the methods of numerical integration of equations did not open the road to the general theory since these methods yield only one particular solution and this solution is obtained on a finite interval. Applications - especially the problems of celestial mechanics - required the clarification of at least the nature of the behavior of integral curves in the entire domain of their existence without integration of the equation. In this connection, at the end of the last century there arose the qualitative theory of differential equations, the creators of which one must by all rights consider to be H. Poincare and A. M. Lyapunov.
Author |
: John A. Walker |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 244 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9781468410365 |
ISBN-13 |
: 1468410369 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Dynamical Systems and Evolution Equations by : John A. Walker
This book grew out of a nine-month course first given during 1976-77 in the Division of Engineering Mechanics, University of Texas (Austin), and repeated during 1977-78 in the Department of Engineering Sciences and Applied Mathematics, Northwestern University. Most of the students were in their second year of graduate study, and all were familiar with Fourier series, Lebesgue integration, Hilbert space, and ordinary differential equa tions in finite-dimensional space. This book is primarily an exposition of certain methods of topological dynamics that have been found to be very useful in the analysis of physical systems but appear to be well known only to specialists. The purpose of the book is twofold: to present the material in such a way that the applications-oriented reader will be encouraged to apply these methods in the study of those physical systems of personal interest, and to make the coverage sufficient to render the current research literature intelligible, preparing the more mathematically inclined reader for research in this particular area of applied mathematics. We present only that portion of the theory which seems most useful in applications to physical systems. Adopting the view that the world is deterministic, we consider our basic problem to be predicting the future for a given physical system. This prediction is to be based on a known equation of evolution, describing the forward-time behavior of the system, but it is to be made without explicitly solving the equation.
Author |
: Robert L. Devaney |
Publisher |
: Springer Nature |
Total Pages |
: 278 |
Release |
: 2021-09-23 |
ISBN-10 |
: 9789811601743 |
ISBN-13 |
: 9811601747 |
Rating |
: 4/5 (43 Downloads) |
Synopsis Topological Dynamics and Topological Data Analysis by : Robert L. Devaney
This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.
Author |
: Somashekhar A. Naimpally |
Publisher |
: World Scientific |
Total Pages |
: 294 |
Release |
: 2013 |
ISBN-10 |
: 9789814407663 |
ISBN-13 |
: 9814407666 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Topology with Applications by : Somashekhar A. Naimpally
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.