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Knots and Links in Three-Dimensional Flows

  • Book
  • © 1997

Overview

Authors:
  1. Robert W. Ghrist
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  2. Philip J. Holmes
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  3. Michael C. Sullivan
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1654)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 1-4

  3. Prerequisites

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 5-32

  4. Templates

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 33-68

  5. Template theory

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 69-106

  6. Bifurcations

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 107-142

  7. Invariants

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 143-166

  8. Concluding remarks

    • Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan
    Pages 167-191

  9. Back Matter

    Pages 192-209
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Keywords

About this book

The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-smale, Smale, and integrable Hamiltonian flows. The necesssary background theory is sketched; however, some familiarity with low-dimensional topology and differential equations is assumed.

Bibliographic Information

  • Book Title: Knots and Links in Three-Dimensional Flows

  • Authors: Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093387

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-62628-2Published: 20 March 1997

  • eBook ISBN: 978-3-540-68347-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 214

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

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