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Bifurcation Phenomena in Mathematical Physics and Related Topics

Proceedings of the NATO Advanced Study Institute held at Cargèse, Corsica, France, June 24–July 7, 1979

  • Claude Bardos
  • Daniel Bessis

Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 54)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Bifurcation in Mathematics and Applications

    1. Front Matter
      Pages 1-1
    2. Michael G. Crandall, Paul H. Rabinowitz
      Pages 3-46
  3. Bifurcation in Theoritical Physics and Statistical Mechanics; Applications

  4. Yang-Mills Field Theory

    1. Front Matter
      Pages 217-217
    2. R. T. Glassey, W. A. Strauss
      Pages 231-241
    3. Basilis Gidas
      Pages 243-267
  5. Solitons in Physics and in Algebraic Geometry

  6. Nonlinear Partial Differential Equations and Applications

  7. Back Matter
    Pages 585-596

About these proceedings

Introduction

One of the main ideas in organizing the Summer Institute of Cargese on "Bifurcation Phenomena in Mathematical Physics and Related Topics" was to bring together Physicists and Mathematicians working on the properties arising from the non linearity of the phenomena and of the models that are used for their description. Among these properties the existence of bifurcations is one of the most interesting, and we had a general survey of the mathematical tools used in this field. This survey was done by M. Crandall and P. Rabinowitz and the notes enclosed in these proceedings were written by E. Buzano a]ld C. Canuto. Another mathematical approach, using Morse Theory was given by J. Smoller reporting on a joint work with C. Conley. An example of a direct application was given by M. Ghil. For physicists the theory of bifurcation is closely related to critical phenomena and this was explained in a series of talks given by J.P. Eckmann, G. Baker and M. Fisher. Some related ideas can be found in the talk given by T. T. Wu , on a joint work with Barry Mc Coy on quantum field theory. The description of these phenomena leads to the use of Pade approximants (it is explained for instance in the lectures of J. Nuttall) and then to some problems in drop hot moment problems. (cf. the lecture of D. Bessis).

Keywords

Diffusion Renormalization group Theoretical physics inverse scattering theory mathematical physics scattering theory

Editors and affiliations

  • Claude Bardos
    • 1
  • Daniel Bessis
    • 2
  1. 1.Départment de MathematiquesUniversité de Paris-NordVilletaneuseFrance
  2. 2.CEN, CEA-SaclayGif-sur-YvetteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-9004-3
  • Copyright Information Springer Science+Business Media B.V. 1980
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-009-9006-7
  • Online ISBN 978-94-009-9004-3
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site
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