Spaces of Dynamical Systems
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Sergei Yu. Pilyugin
About this book
Author / Editor information
Sergei Yu. Pilyugin, St. Petersburg State University, Russia.
Reviews
Reviews of 1rst edition:
__"A book based on 30 years of teaching experience and therefore didactically and logically composed."
In: Enseignement Mathematique 2/2012
__"In the reviewer's opinion, in view of the numerical study of nonlinear systems, this book would be very useful to, in particular, engineers, physicists and economists who want to study the systems in a numerical way."
Mathematical Reviews
__"The main strength of this book is that the author includes complete proofs of results that other publications frequently leave to the reader. […] Altogether, this text is for serious readers that would like a clean and rigorous introduction to the results and methods of proof in dynamical systems. It would make a valuable addition as a reference text to the collection of any academician working in related fields."
Zentralblatt für Mathematik
Topics
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Frontmatter
I -
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Contents
V -
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Preface to the first edition
IX -
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Preface to the second edition
XIII -
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List of main symbols
XV -
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1. Dynamical systems
1 -
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2. Topologies on spaces of dynamical systems
16 -
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3. Equivalence relations
26 -
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4. Hyperbolic fixed point
37 -
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5. Hyperbolic rest point and hyperbolic closed trajectory
66 -
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6. Transversality
77 -
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7. Hyperbolic sets
90 -
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8. Anosov diffeomorphisms
116 -
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9. Smale’s horseshoe and chaos
123 -
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10. Closing lemma
131 -
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11. C0-generic properties of dynamical systems
136 -
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12. Shadowing of pseudotrajectories in dynamical systems
153 -
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13. Invariant measures
174 -
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A. Scheme of the proof of the Mañé theorem
196 -
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B. Lectures on selected chapters of the history of differential equations and dynamical systems
206 -
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Bibliography
236 -
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Index
239
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