Spaces of Dynamical Systems
Description
Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion.
In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories are covered, as well as nonlinearity. The author is an experienced book writer and his work is based on years of teaching.
Reviews / Votes
"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
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Content
Preface
Nomenclature
Contents
Chapter 1. Dynamical systems
Chapter 2. Topologies on spaces of dynamical systems
Chapter 3. Equivalence relations
Chapter 4. Hyperbolic fixed point
Chapter 5. Hyperbolic rest point and hyperbolic closed trajectory
Chapter 6. Transversality
Chapter 7. Hyperbolic sets
Chapter 8. Anosov diffeomorphisms
Chapter 9. Smale's horseshoe and chaos
Chapter 10. Closing Lemma
Chapter 11. C0-generic properties of dynamical systems
Chapter 12. Shadowing of pseudotrajectories in dynamical systems
Appendix A. Scheme of the proof of the Mañé theorem
Appendix B. Lectures on the history of differential equations and dynamical systems
Bibliography
Index
