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Flows on 2-dimensional Manifolds

An Overview

  • Book
  • © 1999

Overview

Authors:
  1. Igor Nikolaev
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  2. Evgeny Zhuzhoma
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1705)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Definitions and examples

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 1-21

  3. Poincaré-Bendixson’s theory

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 23-39

  4. Decomposition of flows

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 41-62

  5. Local theory

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 63-71

  6. Space of flows and vector fields

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 73-93

  7. Ergodic theory

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 95-114

  8. Invariants of surface flows

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 115-174

  9. C*-algebras of surface flows

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 175-199

  10. Semi-local theory

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 201-208

  11. Anosov-Weil problem

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 209-237

  12. Non-compact surfaces

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 239-255

  13. Triptych

    • Igor Nikolaev, Evgeny Zhuzhoma
    Pages 257-268

  14. Back Matter

    Pages 269-295
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Keywords

About this book

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.

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