Introduction To Topological Dynamics
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Introduction To Topological Dynamics
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Author : Konstantin Sergeevich Sibirskii
language : en
Publisher: Springer
Release Date : 1975
Introduction To Topological Dynamics written by Konstantin Sergeevich Sibirskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
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.
Introduction To Topological Dynamics
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Author : Konstantin Sergeevich Sibirskii
language : en
Publisher: Springer
Release Date : 2014-01-14
Introduction To Topological Dynamics written by Konstantin Sergeevich Sibirskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-14 with Mathematics categories.
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.
Minimal Sets
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Author : Walter Helbig Gottschalk
language : en
Publisher:
Release Date : 1958
Minimal Sets written by Walter Helbig Gottschalk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Set theory categories.
A survey of some of the results, models, and problems of topological dynamics. For simplicity of presentation, attention is mostly confined to flows.
Introduction To Topological Dynamics
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Author : K. S. Sibirskij
language : nl
Publisher:
Release Date : 1975
Introduction To Topological Dynamics written by K. S. Sibirskij and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Topological Dynamical Systems
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Author : Jan Vries
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-22
Topological Dynamical Systems written by Jan Vries and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
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.
Introduction To Topological Dynamical Systems Ii
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Author : Mohammed Nokhas Murad Kaki
language : en
Publisher:
Release Date : 2017-04-30
Introduction To Topological Dynamical Systems Ii written by Mohammed Nokhas Murad Kaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-30 with categories.
Introduction To Dynamical Systems
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Author : Michael Brin
language : en
Publisher: Cambridge University Press
Release Date : 2002-10-14
Introduction To Dynamical Systems written by Michael Brin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-14 with Mathematics categories.
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 such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.
Dynamical Systems And Ergodic Theory
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Author : Mark Pollicott
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).
Dynamical Systems
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Author : Luis Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-02
Dynamical Systems written by Luis Barreira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
Local Flows
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Author : J.M. Aarts
language : en
Publisher:
Release Date : 1993
Local Flows written by J.M. Aarts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
