Flows on 2-dimensional Manifolds An Overview /

• Main Authors: Nikolaev, Igor (Author, http://id.loc.gov/vocabulary/relators/aut), Zhuzhoma, Evgeny (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.
• Edition: 1st ed. 1999.
• Series: Lecture Notes in Mathematics, 1705
• Subjects: Geometry.; Mathematical analysis.; Analysis (Mathematics).; Global analysis (Mathematics).; Manifolds (Mathematics).; Dynamics.; Ergodic theory.; Combinatorics.; Analysis.; Global Analysis and Analysis on Manifolds.; Dynamical Systems and Ergodic Theory.

Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of s...

Table of Contents:

• Definitions and examples
• Poincaré-Bendixson's theory
• Decomposition of flows
• Local theory
• Space of flows and vector fields
• Ergodic theory
• Invariants of surface flows
• C *-algebras of surface flows
• Semi-local theory
• Anosov-Weil problem
• Non-compact surfaces
• Triptych.