Introduction To Topological Dynamics
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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 |
: 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 |
: Jan Vries |
Publisher |
: Walter de Gruyter |
Total Pages |
: 516 |
Release |
: 2014-01-31 |
ISBN-10 |
: 9783110342406 |
ISBN-13 |
: 3110342405 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Topological Dynamical Systems by : Jan Vries
There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.
Author |
: Ethan Akin |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 292 |
Release |
: 1997-07-31 |
ISBN-10 |
: 0306455501 |
ISBN-13 |
: 9780306455506 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Recurrence in Topological Dynamics by : Ethan Akin
This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. The theory is implicit in such seminal works as Hillel Furstenberg's Recurrence in Ergodic Theory and Combinational Number Theory, but Ethan Akin's study elaborates it in detail, defining such elements of theory as: open families of special subsets the unification of several ideas associated with transitivity, ergodicity, and mixing the Ellis theory of enveloping semigroups for compact dynamical systems and new notions of equicontinuity, distality, and rigidity.
Author |
: Walter Helbig Gottschalk |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 184 |
Release |
: 1955-01-01 |
ISBN-10 |
: 0821874691 |
ISBN-13 |
: 9780821874691 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Topological Dynamics by : Walter Helbig Gottschalk
Topological dynamics is the study of transformation groups with respect to those topological properties whose prototype occurred in classical dynamics. In this volume, Part One contains the general theory. Part Two contains notable examples of flows which have contributed to the general theory of topological dynamics and which have in turn have been illuminated by the general theory of topological dynamics.
Author |
: Ethan Akin |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 273 |
Release |
: 1993 |
ISBN-10 |
: 9780821849323 |
ISBN-13 |
: 0821849328 |
Rating |
: 4/5 (23 Downloads) |
Synopsis The General Topology of Dynamical Systems by : Ethan Akin
Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.
Author |
: Konstantin Sergeevich Sibirskii |
Publisher |
: Springer |
Total Pages |
: 0 |
Release |
: 2014-01-14 |
ISBN-10 |
: 9401023085 |
ISBN-13 |
: 9789401023085 |
Rating |
: 4/5 (85 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 |
: Walter Helbig Gottschalk |
Publisher |
: |
Total Pages |
: 54 |
Release |
: 1958 |
ISBN-10 |
: UOM:39015095253350 |
ISBN-13 |
: |
Rating |
: 4/5 (50 Downloads) |
Synopsis Minimal Sets by : Walter Helbig Gottschalk
A survey of some of the results, models, and problems of topological dynamics. For simplicity of presentation, attention is mostly confined to flows.
Author |
: Manfred Einsiedler |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 486 |
Release |
: 2010-09-11 |
ISBN-10 |
: 9780857290212 |
ISBN-13 |
: 0857290215 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Ergodic Theory by : Manfred Einsiedler
This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
Author |
: Michael Brin |
Publisher |
: Cambridge University Press |
Total Pages |
: 0 |
Release |
: 2015-11-05 |
ISBN-10 |
: 1107538947 |
ISBN-13 |
: 9781107538948 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Introduction to Dynamical Systems by : Michael Brin
This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.