Bifurcation Phenomena in Mathematical Physics and Related Topics: Proceedings of the NATO Advanced Study Institute Held at Cargèse, Corsica, France, June 24–July 7, 1979Claude Bardos, D. Bessis 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). |
Contents
G Crandall and P H Rabinowitz Notes by E Buzano | 3 |
Conley and J Smoller Remarks on the Stability | 47 |
Ghil Successive Bifurcations and the IceAge Problem | 57 |
Copyright | |
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Common terms and phrases
algebraic analytic assume asymptotic Banach space behavior Bessis eds bifurcation diagram Bifurcation Phenomena boundary Chudnovsky classical coefficients condition conservation laws consider constant convergence corresponding critical points curve defined deformation density dimensional eigenvalue electrons energy example exists exponents finite fixed point gauge gauge theory Green's functions Hamiltonian hull function Implicit Function Theorem infinite Ising model lectures Lemma Lett linear differential equations mapping Math matrix method monodromy Nonlinear obtained operator Padé approximants Painlevé parameter periodic solutions perturbation phase Phenomena in Mathematical Phys Physics and Related polynomial potential problem proof quantum field theory RABINOWITZ renormalisation renormalization group Riemann satisfies singular Slater determinant soliton stability zones stable statistical mechanical TDHF Theorem Thirring model tion transformation trivial unstable variables vector zero μν