Pilyugin Spaces of Dynamical Systems

1. Auflage 2012
ISBN: 978-3-11-025841-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 3, 244 Seiten

Reihe: De Gruyter Studies in Mathematical Physics

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.

Zielgruppe

Mathematical and Theoretical Physicists, Mathematicians, Scientists working with Applications of Dynamical Systems, Students

Autoren/Hrsg.

Pilyugin, Sergei Yu.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

Frontmatter
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

Über Autor(innen)

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