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• catalog abstract "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.".
• catalog contributor b6130102.
• catalog created "1994.".
• catalog date "1994".
• catalog date "1994.".
• catalog dateCopyrighted "1994.".
• catalog description "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.".
• catalog description "Includes bibliographical references and index.".
• catalog description "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.".
• catalog extent "viii, 188 p. :".
• catalog hasFormat "Space of dynamical systems with the C⁰-topology.".
• catalog identifier "3540577025 :".
• catalog isFormatOf "Space of dynamical systems with the C⁰-topology.".
• catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1571".
• catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1571".
• catalog issued "1994".
• catalog issued "1994.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer-Verlag,".
• catalog relation "Space of dynamical systems with the C⁰-topology.".
• catalog subject "510 s 514/.71 20".
• catalog subject "Differentiable dynamical systems.".
• catalog subject "Global analysis (Mathematics).".
• catalog subject "Global differential geometry.".
• catalog subject "Mathematics.".
• catalog subject "Perturbation (Mathematics)".
• catalog subject "QA3 .L28 no. 1571 QA614.87".
• catalog subject "Stability.".
• catalog tableOfContents "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.".
• catalog title "The space of dynamical systems with the C⁰-topology / Sergei Yu. Pilyugin.".
• catalog type "text".