CiNii 図書 - International workshop on symmetry and perturbation theory (SPT-98), Rome 16-22 December 1998

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.

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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International workshop on symmetry and perturbation theory (SPT-98), Rome 16-22 December 1998

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