Dynamical Systems on 2- and 3-Manifolds

• Κύριοι συγγραφείς: Grines, Viacheslav Z. (Συγγραφέας), Medvedev, Timur V. (Συγγραφέας), Pochinka, Olga V. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Σειρά: Developments in Mathematics, 46
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Topology.; Dynamical Systems and Ergodic Theory.; Ordinary Differential Equations.

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly f...

Πίνακας περιεχομένων:

• List of Symbols
• Introduction
• Further reading
• 1. Introduction to dynamical systems
• 2. General properties of the Morse-Smale diffeomorphisms
• 3. The topological classification of the gradient-like diffeomorphism on surfaces
• 4. Wild embedding on the separatrices into 3-manifolds and Pixton diffeomorphism
• 5. The classification of the gradient-like diffeomorphisms on 3-manifolds
• 6. Interrelation between the dynamics of Morse-Smale diffeormorphisms and the topology of the ambient 3-manifold
• 7. An energy function for Morse-Smale diffeomorphisms on 3-manifolds
• 8. The properties of nontrivial basic sets of A-diffeomorphisms related to type and dimension
• 9. The classification of nontrivial basic sets of A-diffeomorphisms of surfaces
• 10. Basic topological concepts of dynamical systems
• Index.