The space of dynamical systems with the C⁰-topology /

The space of dynamical systems with the C⁰-topology /

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Bibliographic Details
Author / Creator:Pilyugin, Sergei Yu. (Sergei Yurievitch), 1947-
Imprint:Berlin ; New York : Springer-Verlag, ©1994.
Description:1 online resource (viii, 188 pages) : illustrations.
Language:English
Series:Lecture notes in mathematics, 0075-8434 ; 1571
Lecture notes in mathematics (Springer-Verlag) ; 1571.
Subject:
Differentiable dynamical systems.
Perturbation (Mathematics)
Stability.
Differentiable dynamical systems.
Perturbation (Mathematics)
Stability.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11071343
Hidden Bibliographic Details
ISBN:9783540483144
3540483144
9783540577027
3540577025
9780387577029
0387577025
Notes:Includes bibliographical references (pages 183-186) and index.
Restrictions unspecified
Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212
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Print version record.
Summary: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.
Other form:Print version: Pilyugin, Sergei Yu. (Sergei Yurievitch), 1947- Space of dynamical systems with the C⁰-topology. Berlin ; New York : Springer-Verlag, ©1994 3540577025
Table of Contents:
  • Ch. 0. Definitions and Preliminary Results. 0.1. Spaces of Dynamical Systems. 0.2. The Space M[superscript *]. 0.3. The C[superscript 0]-Closing Lemma. 0.4. Hyperbolic Sets
  • Ch. 1. Generic Properties of Dynamical Systems. 1.1. Tolerance Stability. 1.2. Pseudotrajectories. 1.3. Prolongations. 1.4. Returning Points and Filtrations
  • Ch. 2. Topological Stability. 2.1. General Properties of Topologically Stable Systems. 2.2. Topological Stability of Systems with Hyperbolic Structure. 2.3. Topologically Stable Dynamical Systems on the Circle.

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