Regular deformations of completely integrable systems

DOI10.4310/JSG.2005.V3.N1.A1zbMATH Open1092.37034arXivmath/0504379MaRDI QIDQ2491049

Nicolas Roy

Publication date: 19 May 2006

Published in: The Journal of Symplectic Geometry (Search for Journal in Brave)

Abstract: We study several aspects of the regular deformations of completely integrable systems. Namely, we prove the existence of a Hamiltonian normal form for these deformations and we show the necessary and sufficient conditions a perturbation has to satisfy in order for the perturbed Hamiltonian to be a first order deformation.

Full work available at URL: https://arxiv.org/abs/math/0504379

zbMATH Keywords

perturbationcompletely integrable systemsfirst-order deformationHamiltonian normal form

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Momentum maps; symplectic reduction (53D20)

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