The Space of Dynamical Systems with the C0-Topology
The Space of Dynamical Systems with the C0-Topology

Author: Sergei Yu. Pilyugin

Publisher: Springer

Published: 2006-11-15

Total Pages: 197

ISBN-13: 3540483144

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This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!)-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Co(upper index!)-generic properties of dynamical systems, topological stability, perturbations of attractors, limit sets of domains are discussed. The book contains some new results (Lipschitz shadowing of pseudotrajectories in structurally stable diffeomorphisms for instance). The aim of the author was to simplify and to "visualize" some basic proofs, so the main part of the book is accessible to graduate students in pure and applied mathematics. The book will also be a basic reference for researchers in various fields of dynamical systems and their applications, especially for those who study attractors or pseudotrajectories generated by numerical methods.

Topological Theory of Dynamical Systems
Topological Theory of Dynamical Systems

Author: N. Aoki

Publisher: Elsevier

Published: 1994-06-03

Total Pages: 425

ISBN-13: 008088721X

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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.

The User's Approach to Topological Methods in 3D Dynamical Systems
The User's Approach to Topological Methods in 3D Dynamical Systems

Author: Mario A. Natiello

Publisher: World Scientific

Published: 2007

Total Pages: 142

ISBN-13: 9812771484

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This book presents the development and application of some topological methods in the analysis of data coming from 3D dynamical systems (or related objects). The aim is to emphasize the scope and limitations of the methods, what they provide and what they do not provide. Braid theory, the topology of surface homeomorphisms, data analysis and the reconstruction of phase-space dynamics are thoroughly addressed.

The General Topology of Dynamical Systems
The General Topology of Dynamical Systems

Author: Ethan Akin

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 273

ISBN-13: 0821849328

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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 Dynamical Systems
Topological Dynamical Systems

Author: Jan Vries

Publisher: Walter de Gruyter

Published: 2014-01-31

Total Pages: 516

ISBN-13: 3110342405

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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.

Invitation to C*-algebras and Topological Dynamics
Invitation to C*-algebras and Topological Dynamics

Author: Jun Tomiyama

Publisher: World Scientific

Published: 1987

Total Pages: 180

ISBN-13: 9789971503383

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This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to the readers the subject in an elementary way, including also results of recent developments.

Recurrence in Topological Dynamics
Recurrence in Topological Dynamics

Author: Ethan Akin

Publisher: Springer Science & Business Media

Published: 1997-07-31

Total Pages: 292

ISBN-13: 9780306455506

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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.