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The General Topology of Dynamical Systems

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 328/5 ( reviews)

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Book Synopsis The General Topology of Dynamical Systems by : Ethan Akin

Download or read book The General Topology of Dynamical Systems written by Ethan Akin. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topological Theory of Dynamical Systems

1994-06-03 Mathematics
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Release : 1994-06-03
Genre : Mathematics
Kind : eBook
Book Rating : 21X/5 ( reviews)

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Book Synopsis Topological Theory of Dynamical Systems by : N. Aoki

Download or read book Topological Theory of Dynamical Systems written by N. Aoki. This book was released on 1994-06-03. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.

Topological Dynamical Systems

2014-01-31 Mathematics
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Release : 2014-01-31
Genre : Mathematics
Kind : eBook
Book Rating : 405/5 ( reviews)

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Book Synopsis Topological Dynamical Systems by : Jan Vries

Download or read book Topological Dynamical Systems written by Jan Vries. This book was released on 2014-01-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Theory of Dynamical Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 034/5 ( reviews)

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Book Synopsis Geometric Theory of Dynamical Systems by : J. Jr. Palis

Download or read book Geometric Theory of Dynamical Systems written by J. Jr. Palis. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: ... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.

Recent Progress in General Topology III

2013-12-11 Mathematics
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Release : 2013-12-11
Genre : Mathematics
Kind : eBook
Book Rating : 24X/5 ( reviews)

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Book Synopsis Recent Progress in General Topology III by : K.P. Hart

Download or read book Recent Progress in General Topology III written by K.P. Hart. This book was released on 2013-12-11. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

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