Spaces of Dynamical Systems

Auteur

Sergei Yu. Pilyugin, St. Petersburg State University, Russia.

Texte du rabat

This updated revision conveys the modern theory of dynamical systems in a comprehensible and didactically structure based on many years of teaching. The work covers the current research of topological dynamics, structural stability, chaotic dynamics and generic properties including complete proofs of presented results. New coverage of Invariant Measures.

Résumé

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

Contenu
Frontmatter -- Contents -- Preface to the first edition -- Preface to the second edition -- List of main symbols -- 1. Dynamical systems -- 2. Topologies on spaces of dynamical systems -- 3. Equivalence relations -- 4. Hyperbolic fixed point -- 5. Hyperbolic rest point and hyperbolic closed trajectory -- 6. Transversality -- 7. Hyperbolic sets -- 8. Anosov diffeomorphisms -- 9. Smale's horseshoe and chaos -- 10. Closing lemma -- 11. C0-generic properties of dynamical systems -- 12. Shadowing of pseudotrajectories in dynamical systems -- 13. Invariant measures -- A. Scheme of the proof of the Mañé theorem -- B. Lectures on selected chapters of the history of differential equations and dynamical systems -- Bibliography -- Index