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

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). Front Matter....Pages i-ix Front Matter....Pages 1-1 Mathematical Theory of Bifurcation....Pages 3-46 Remarks on the Stability of Steady-State Solutions of Reaction-Diffusion Equations....Pages 47-56 Successive Bifurcations and the Ice-Age Problem....Pages 57-58 Front Matter....Pages 59-59 Critical Phenomena in Statistical Mechanics — Aspects of Renormalization Group Theory....Pages 61-68 Lattice Renormalization of Non-Perturbative Quantum Field Theory....Pages 69-90 The Continuous-Spin, Ising Model of Field Theory and the Renormalization Group....Pages 91-114 Bifurcations for Maps....Pages 115-135 Critical Properties of One Dimensional Mappings....Pages 137-154 Intermittency: A Simple Mechanism of Continuous Transition from Order to Chaos....Pages 155-162 Metal-Insulator Transition in One-Dimensional Deformable Lattices....Pages 163-184 Sets of Minimum Capacity, Padé Approximants and the Bubble Problem....Pages 185-201 Bifurcations in the Diophant Moment Problem....Pages 203-215 Front Matter....Pages 217-217 Yang-Mills Fields: Semi Classical Aspects....Pages 219-229 Propagation of the Energy of Yang-Mills Fields....Pages 231-241 Euclidean Yang-Mills and Related Equations....Pages 243-267 Existence of Stationary States in Nonlinear Scalar Field Equations....Pages 269-292 Front Matter....Pages 293-293 Solitons: Inverse Scattering Theory and Its Applications....Pages 295-349 New Results on the Nonlinear Boltzmann Equation....Pages 351-370 Solvable Many-Body Problems and Related Mathematical Findings (and Conjectures)....Pages 371-384 Riemann Monodromy Problem, Isomonodromy Deformation Equations and Completely Integrable Systems....Pages 385-447 Front Matter....Pages 293-293 Padé Approximation and the Riemann Monodromy Problem....Pages 449-510 Front Matter....Pages 511-511 Non Linear Evolution Equations of Schrodinger Type....Pages 513-520 Asymptotic Behavior of Solutions of Hyperbolic Balance Laws....Pages 521-533 Nonlinear Problems Arising in the Study of Nematic Liquid Crystals....Pages 535-550 Some Properties of Functional Invariant Sets for Navier-Stokes Equations....Pages 551-554 An Introduction to the Time-Dependent Hartree-Fock Theory in Nuclear Physics....Pages 555-583 Back Matter....Pages 585-596