International workshop on symmetry and perturbation theory (SPT-98), Rome 16-22 December 1998
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Bibliographic Information
International workshop on symmetry and perturbation theory (SPT-98), Rome 16-22 December 1998
World Scientific, c1999
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Symmetry and perturbation theory (SPT-98)
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Includes bibliographical references
Description and Table of Contents
Description
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 students and newcomers to the field a rapid introduction to some active themes of research and recent results in symmetry and perturbation theory.
Table of Contents
- Nonlinear symmetries and normal forms, G. Cicogna and G. Gaeta
- asymptotic integrability, A. Degasperis and M. Procesi
- families of relative equilibria in Hamiltonian systems with dissipation, G. Derks
- on averaging methods for partial differential equations, F. Verhulst
- the geometrical description of hyperelliptically separable systems, S. Abenda and Y. Federov
- smooth seminormal forms of symmetric and reversible systems, P. Bonckaert
- convergent normal forms, bifurcations and symmetries, G. Cicogna
- perturbing a symmetric resonance - the magnetic spherical pendulum, J. Montaldi
- symmetry reductions and periodic orbits in the planar three-body problem, L. Sbano
- simultaneous normal forms of commuting maps and vector fields, M. Yoshino
- interlaced branching equations and invariance in the theory of nonlinear equations, N.A. Sidorov and V.R. Abdullin. (Part contents)
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