Bi-Hamiltonian partially integrable systems
Dynamical Systems
2015-06-26 v4 Mathematical Physics
math.MP
Abstract
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact) invariant manifold which makes this dynamical system into a partially integrable Hamiltonian system. This Poisson structure is by no means unique. Bi-Hamiltonian partially integrable systems are described in some detail. As an outcome, we state the conditions of quasi-periodic stability (the KAM theorem) for partially integrable Hamiltonian systems.
Cite
@article{arxiv.math/0211463,
title = {Bi-Hamiltonian partially integrable systems},
author = {G. Giachetta and L. Mangiarotti and G. Sardanashvily},
journal= {arXiv preprint arXiv:math/0211463},
year = {2015}
}
Comments
18 pages