Compactification of actions of \(\mathbb{R}^ k\) and Hamiltonian systems of toric type
type: Item
instance of: scholarly article
title: Compactification of actions of \(\mathbb{R}^ k\) and Hamiltonian systems of toric type
zbMATH Open document ID: 0832.58016
DOI: 10.1016/0019-3577(95)91245-Q
published in: Indagationes Mathematicae. New Series
publication date: 1995-10-09T00:00:00Z
review text: Let \((M, \omega, H)\) be an Hamiltonian system endowed with a finite- dimensional space \(\mathcal A\) of first integral. The center of \(\mathcal A\) for the Poisson bracket defines an infinitesimal Hamiltonian action of \(\mathbb{R}^k\) on \(M\). Under the condition that \(\mathcal O\) is a compact orbit of this action, the author gives a necessary and sufficient condition for the system to admit a normal form of toric type in a neighborhood at \(\mathcal O\). This result generalizes the theorems of Arnol'd-Liouville, Eliasson, Nekhoroshev and its version with singularities. The key of the proof is a criterion of compactification for \(\mathbb{R}^k\)-actions which extends a result of J.-P. Dufour and P. Molino.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37G05
zbMATH DE Number: 792827
zbMATH Keywords: first integral
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: normal form
author: Alain R. Veeravalli
reviewed by: Yoshihide Kozai
MaRDI profile type: Publication
cites work: Q4166257
cites work: Q3981123
cites work: Q3973388
cites work: Lectures on groups of transformations. Notes by R. R. Simha and R. Sridharan
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q3361942
cites work: Q4771891
cites work: Lifting smooth homotopies of orbit spaces
cites work: Q3142953
full work available at URL: 0019-3577(95)91245-q
OpenAlex ID: W2089952179
description: scientific article; zbMATH DE number 792827