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Bifurcation and Symmetry

Cross Influence between Mathematics and Applications

  • Book
  • © 1992

Overview

Editors:
  1. Eugene L. Allgower

    1. Dept. of Mathematics, Colorado State University, Fort Collins, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Klaus Böhmer

    1. Fachbereich Mathematik, Universität Marburg, Marburg, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Martin Golubitsky

    1. Dept. of Mathematics, University of Houston, Houston, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 104)

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Table of contents (28 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Exploiting Equivariance in the Reduced Bifurcation Equations

    • Eugene L. Allgower, Klaus Böhmer, Mei Zhen
    Pages 1-10

  3. The homoclinic twist bifurcation point

    • D. G. Aronson, S. A. van Gils, M. Krupa
    Pages 11-22

  4. High Corank Steady-State Mode Interactions on a Rectangle

    • Peter Ashwin
    Pages 23-33

  5. Numerical Investigation of the Bifurcation from Travelling Waves to Modulated Travelling Waves

    • P. Aston, A. Spence, W. Wu
    Pages 35-47

  6. Mode Interactions of an Elliptic System on the Square

    • Klaus Böhmer, Mei Zhen
    Pages 49-58

  7. Secondary, Tertiary and Quarternary States of Fluid Flow

    • F. H. Busse, R. M. Clever
    Pages 59-73

  8. Hopf-type bifurcations in the presence of linear and nonlinear symmetries

    • G. Cicogna
    Pages 75-83

  9. On Diffusively Coupled Oscillators

    • Gerhard Dangelmayr, Michael Kirby
    Pages 85-97

  10. Mechanisms of Symmetry Creation

    • Michael Dellnitz, Martin Golubitsky, Ian Melbourne
    Pages 99-109

  11. Generic Bifurcations of Pendula

    • Michael Dellnitz, Jerrold E. Marsden, Ian Melbourne, Jürgen Scheurle
    Pages 111-122

  12. Symmetry Aspects of 3-Periodic Minimal Surfaces

    • Werner Fischer, Elke Koch
    Pages 123-133

  13. Hopf bifurcation at non-semisimple eigenvalues: a singularity theory approach

    • J. E. Furter
    Pages 135-145

  14. On Trigonometric Collocation in Hopf Bifurcation

    • Eckart W. Gekeler
    Pages 147-156

  15. Exploiting Symmetry in Solving Linear Equations

    • Kurt Georg, Rick Miranda
    Pages 157-168

  16. Symmetry and Preservation of Nodal Structure in Elliptic Equations Satisfying Fully Nonlinear Neumann Boundary Condtions

    • Timothy J. Healey, Hansjörg Kielhofer
    Pages 169-177

  17. A New Approach for Solving Singular Nonlinear Equations

    • Annegret Hoy
    Pages 179-189

  18. Quasiperiodic drift flow in the Couette-Taylor problem

    • P. Laure, J. Menck, J. Scheurle
    Pages 191-202

  19. Numerical applications of equivariant reduction techniques

    • Vladimír Janovský, Petr Plecháč
    Pages 203-213

  20. Numerical Bifurcation Analysis of a Model of Coupled Neural Oscillators

    • Alexander I. Khibnik, Roman M. Borisyuk, Dirk Roose
    Pages 215-228
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Keywords

About this book

Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre­ sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps­ University of Marburg, Germany.

Editors and Affiliations

  • Dept. of Mathematics, Colorado State University, Fort Collins, USA

    Eugene L. Allgower

  • Fachbereich Mathematik, Universität Marburg, Marburg, Germany

    Klaus Böhmer

  • Dept. of Mathematics, University of Houston, Houston, USA

    Martin Golubitsky

Bibliographic Information

  • Book Title: Bifurcation and Symmetry

  • Book Subtitle: Cross Influence between Mathematics and Applications

  • Editors: Eugene L. Allgower, Klaus Böhmer, Martin Golubitsky

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7536-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1992

  • Hardcover ISBN: 978-3-7643-2739-2Due: 10 April 1992

  • Softcover ISBN: 978-3-0348-7538-7Published: 03 October 2013

  • eBook ISBN: 978-3-0348-7536-3Published: 08 March 2013

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: VI, 327

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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