Functions Whose Poisson Brackets Are Constants
- 1 August 1971
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (8), 1482-1486
- https://doi.org/10.1063/1.1665760
Abstract
A local normal form under canonical transformation is found for n independent functions of 2n variables, with the condition that the Poisson bracket of each pair of the functions be constant. The normal form, closely related to work of Lie, is used to prove a conjecture of Avez on 1-forms in involution and to obtain a criterion for n independent functions of 2n variables to be extendable to a canonical coordinate system. The last result has been obtained in different ways by Lie and Kruskal.Keywords
This publication has 1 reference indexed in Scilit:
- Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly PeriodicJournal of Mathematical Physics, 1962