Flows on 2-dimensional Manifolds

Nikolaev, Igor.

Flows on 2-dimensional Manifolds An Overview / [electronic resource] : by Igor Nikolaev, Evgeny Zhuzhoma. - XXII, 302 p. online resource. - Lecture Notes in Mathematics, 1705 0075-8434 ; . - Lecture Notes in Mathematics, 1705 .

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.

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 surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.

9783540487593

10.1007/BFb0093599 doi


Geometry.
Global analysis (Mathematics).
Global analysis.
Differentiable dynamical systems.
Combinatorics.
Geometry.
Analysis.
Global Analysis and Analysis on Manifolds.
Dynamical Systems and Ergodic Theory.
Combinatorics.

QA440-699

516
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