Flows on 2-dimensional Manifolds An Overview
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 care
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Zbl 1022.37027 Nikolaev, Igor; Zhuzhoma, Evgeny Flows on 2-dimensional manifolds. An overview. (English) Lecture Notes in Mathematics. 1705. Berlin: Springer. xix, 294 p. DM 77.00; ¨ oS 563.00; sFr. 70.50; £29.50; $ 57.00 (1999). ISBN 3-540-66080-1/pbk http://dx.doi.org/10.1007/BFb0093599 http://www.springerlink.com/openurl.asp?genre=journalissn=0075-8434
Publisher’s description: 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 Poincar´e-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 noncompact 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. Keywords : Poincar´e-Bendixson theory; time-evolution in low-dimensional topological spaces; Morse-Smale theories; invariants of surface flows; Anosov-Weil problem; C ∗ algebras; noncompact surfaces Classification : ∗ 37E35 Flows on surfaces 37-02 Research exposition (Dynamical systems and ergodic theory) 37C10 Vector fields, flows, ordinary differential equations
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