Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces
arXiv:1910.08749 · doi:10.1016/j.bulsci.2011.09.005
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.
References in corpus (4)
- Darboux Polynomials and First Integrals of Natural Polynomial Hamiltonian Systems
- Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems
- Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces
- Characterization, global analysis and integrability of a family of Poisson structures