Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces
Mathematical Physics
2019-10-22 v1 Classical Analysis and ODEs
Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Classical Physics
Abstract
In the literature, the existence of Darboux polynomials and additional polynomial first integrals has been considered in the case of Hamiltonian systems. In this article such problem is formulated in the more general framework of Poisson structures, which include Hamiltonian systems as a particular case. This generalization allows a natural extension of the previous results, which can now be applied to a larger class of vector fields and is valid for arbitrary diffeomorphisms (instead of canonical transformations). Examples are discussed.
Cite
@article{arxiv.1910.08749,
title = {Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces},
author = {Isaac A. García and Benito Hernández-Bermejo},
journal= {arXiv preprint arXiv:1910.08749},
year = {2019}
}