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  • Textbook
  • © 1983

Dynamical Systems on Surfaces

Authors:

  1. Claude Godbillon

    1. Département de Mathématiques, Université Louis Pasteur, Strasbourg, France

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Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-vii
    PDF

  2. Vector Fields on Manifolds

    • Claude Godbillon
    Pages 1-38

  3. The Local Behaviour of Vector Fields

    • Claude Godbillon
    Pages 39-74

  4. Planar Vector Fields

    • Claude Godbillon
    Pages 75-129

  6. Vector Fields on Surfaces

    • Claude Godbillon
    Pages 178-199

  7. Back Matter

    Pages 200-204
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About this book

These notes are an elaboration of the first part of a course on foliations which I have given at Strasbourg in 1976 and at Tunis in 1977. They are concerned mostly with dynamical sys­ tems in dimensions one and two, in particular with a view to their applications to foliated manifolds. An important chapter, however, is missing, which would have been dealing with structural stability. The publication of the French edition was re­ alized by-the efforts of the secretariat and the printing office of the Department of Mathematics of Strasbourg. I am deeply grateful to all those who contributed, in particular to Mme. Lambert for typing the manuscript, and to Messrs. Bodo and Christ for its reproduction. Strasbourg, January 1979. Table of Contents I. VECTOR FIELDS ON MANIFOLDS 1. Integration of vector fields. 1 2. General theory of orbits. 13 3. Irlvariant and minimaI sets. 18 4. Limit sets. 21 5. Direction fields. 27 A. Vector fields and isotopies. 34 II. THE LOCAL BEHAVIOUR OF VECTOR FIELDS 39 1. Stability and conjugation. 39 2. Linear differential equations. 44 3. Linear differential equations with constant coefficients. 47 4. Linear differential equations with periodic coefficients. 50 5. Variation field of a vector field. 52 6. Behaviour near a singular point. 57 7. Behaviour near a periodic orbit. 59 A. Conjugation of contractions in R. 67 III. PLANAR VECTOR FIELDS 75 1. Limit sets in the plane. 75 2. Periodic orbits. 82 3. Singular points. 90 4. The Poincare index.
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Keywords

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Authors and Affiliations

  • Département de Mathématiques, Université Louis Pasteur, Strasbourg, France

    Claude Godbillon

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Bibliographic Information

  • Book Title: Dynamical Systems on Surfaces

  • Authors: Claude Godbillon

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-642-68626-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1983

  • Softcover ISBN: 978-3-540-11645-5Published: 01 November 1982

  • eBook ISBN: 978-3-642-68626-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: VIII, 204

  • Topics: Numerical Analysis

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eBook USD 39.99
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  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

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