Spaces of Dynamical Systems

2. rev. and exten. Auflage 2024
ISBN: 978-3-11-064446-3
Verlag: De Gruyter

Buch, Englisch, Band 3, 241 Seiten, HC runder Rücken kaschiert, Format (B × H): 175 mm x 246 mm, Gewicht: 622 g

Reihe: De Gruyter Studies in Mathematical Physics

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.

Zielgruppe

Researchers and teachers of Mathematical and Theoretical Physics

Autoren/Hrsg.

Pilyugin, Sergei Yu.

Piljugin, Sergej Ju.

Fachgebiete

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

Inhaltsverzeichnis

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

Über Autor(innen)

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