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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

  • Conference proceedings
  • © 1980

Overview

Editors:
  1. Claude Bardos

    1. Départment de Mathematiques, Université de Paris-Nord, Villetaneuse, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Daniel Bessis

    1. CEN, CEA-Saclay, Gif-sur-Yvette, France

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 54)

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Table of contents (26 papers)

  1. Front Matter

    Pages i-ix
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  2. Bifurcation in Mathematics and Applications

    1. Front Matter

      Pages 1-1
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    2. Mathematical Theory of Bifurcation

      • Michael G. Crandall, Paul H. Rabinowitz
      Pages 3-46

    3. Remarks on the Stability of Steady-State Solutions of Reaction-Diffusion Equations

      • C. Conley, J. Smoller
      Pages 47-56

    4. Successive Bifurcations and the Ice-Age Problem

      • Michael Ghil
      Pages 57-58

  3. Bifurcation in Theoritical Physics and Statistical Mechanics; Applications

    1. Front Matter

      Pages 59-59
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    2. Critical Phenomena in Statistical Mechanics — Aspects of Renormalization Group Theory

      • Michael E. Fisher
      Pages 61-68

    3. Lattice Renormalization of Non-Perturbative Quantum Field Theory

      • Barry M. Mc Coy, Tai Tsun Wu
      Pages 69-90

    4. The Continuous-Spin, Ising Model of Field Theory and the Renormalization Group

      • George A. Baker Jr.
      Pages 91-114

    5. Bifurcations for Maps

      • J. P. Eckmann
      Pages 115-135

    6. Critical Properties of One Dimensional Mappings

      • Bernard Derrida
      Pages 137-154

    7. Intermittency: A Simple Mechanism of Continuous Transition from Order to Chaos

      • Y. Pomeau
      Pages 155-162

    8. Metal-Insulator Transition in One-Dimensional Deformable Lattices

      • Serge Aubry
      Pages 163-184

    9. Sets of Minimum Capacity, Padé Approximants and the Bubble Problem

      • J. Nuttall
      Pages 185-201

    10. Bifurcations in the Diophant Moment Problem

      • D. Bessis
      Pages 203-215

  4. Yang-Mills Field Theory

    1. Front Matter

      Pages 217-217
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    2. Yang-Mills Fields: Semi Classical Aspects

      • R. Stora
      Pages 219-229

    3. Propagation of the Energy of Yang-Mills Fields

      • R. T. Glassey, W. A. Strauss
      Pages 231-241

    4. Euclidean Yang-Mills and Related Equations

      • Basilis Gidas
      Pages 243-267

    5. Existence of Stationary States in Nonlinear Scalar Field Equations

      • H. Berestycki, P. L. Lions
      Pages 269-292
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Keywords

About this book

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).

Editors and Affiliations

  • Départment de Mathematiques, Université de Paris-Nord, Villetaneuse, France

    Claude Bardos

  • CEN, CEA-Saclay, Gif-sur-Yvette, France

    Daniel Bessis

Bibliographic Information

  • Book Title: Bifurcation Phenomena in Mathematical Physics and Related Topics

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

  • Editors: Claude Bardos, Daniel Bessis

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-009-9004-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1980

  • Hardcover ISBN: 978-90-277-1086-4Published: 31 March 1980

  • Softcover ISBN: 978-94-009-9006-7Published: 13 October 2011

  • eBook ISBN: 978-94-009-9004-3Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: X, 596

  • Topics: Chemistry/Food Science, general

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