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The second workshop on “Symmetry and Perturbation Theory” served as a forum for discussing the relations between symmetry and perturbation theory, and this put in contact rather different communities. The extension of the rigorous results of perturbation theory established for ODE's to the case of nonlinear evolution PDE's was also discussed: here a number of results are known, particularly in connection with (perturbation of) integrable systems, but there is no general frame as solidly established as in the finite-dimensional case. In aiming at such an infinite-dimensional extension, for which standard analytical tools essential in the ODE case are not available, it is natural to look primarily at geometrical and topological methods, and first of all at those based on exploiting the symmetry properties of the systems under study (both the unperturbed and the perturbed ones); moreover, symmetry considerations are in several ways basic to our understanding of integrability, i.e. finally of the unperturbed systems on whose understanding the whole of perturbation theory has unavoidably to rely.This volume contains tutorial, regular and contributed papers. The tutorial papers give ...

This is the fourth conference on “Supersymmetry and Perturbation Theory” (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc. Contents:An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and Schrödinger Equations (S Benenti)Partial Symmetries and Symmetric Sets of Solutions to PDE's (G Cicogna)On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann-Hilbert Problem (V Enolski & T Grava)Bifurcations in Flow-Induced Vibration (S Fatimah & F Verhulst)Steklov-Lyapunov Type Systems (Yu N Fedorov)Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile)On the Linearization of Holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev)Smooth Normalization of a Vector Field Near an Invariant Manifold (A Kopanskii)Inverse Problems for SL(2) Lattices (V B Kuznetsov)Some Remarks about the Geometry of Hamiltonian Conservation Laws (J-P Ortega)Janet's Algorithm (W Plesken)Some Integrable Billiards (E Previato)Symmetries of Relative Equilibria for Simple...

This is the fourth conference on OC Supersymmetry and Perturbation TheoryOCO (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc. Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and SchrAdinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDE's (G Cicogna); On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann-Hilbert Problem (V Enolski & T Grava); Bifurcations in Flow-Induced Vibration (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Yu N Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of Holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); Smooth Normalization of a Vector Field Near an Invariant Manifold (A Kopanskii); Inverse Problems for SL (2) Lattices (V B Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J-P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative...

The third conference on “Symmetry and Perturbation Theory” (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field — more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit. Contents:Geometry and Dynamics of Hyperelliptically Separable Systems (S Abenda)A Functional Analysis Approach to Arnold Diffusion (M Berti)Linearizing Resonant Normal Forms (G Gaeta)Tori Breakdown in Coupled Map Lattices (C Giberti)A Two-Dimensional Version of the Camassa–Holm Equation (H-P Kruse et al.)Generalizations of Gordon's Theorem (N Nekhoroshev)Moving Frames: A Brief Survey (P J Olver)A Symmetric Normal Form for the Fermi Pasta Ulam Chain (B Rink)Higher Order Resonance in Two Degrees of Freedom Hamiltonian System (J M Tuwankotta & F Verhulst)Topologically Unavoidable Degeneracies in Band Structure of Solids (J Zak)and other papers Readership: Graduate students and researchers in mathematics, physics and chemistry. Keywords:Symmetry;Perturbation Theory;Geometry;Dynamics;Hyperelliptically Separable Systems;Arnold Diffusion;Coupled Map Lattices;Gordon's Theorem;Fermi...

The third conference on ?Symmetry and Perturbation Theory? (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field ? more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit.

M. Brelot: Historical introduction.- H. Bauer: Harmonic spaces and associated Markov processes.- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel.- J. Deny: Méthodes hilbertiennes en theory du potentiel.- J.L. Doob: Martingale theory – Potential theory.- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés.