Polynomial and rational integrability of polynomial Hamiltonian systems

Abstract

Agraïments/Ajudes: The third author was partially supported by FCT through CAMGDS, Lisbon.

Within the class of canonical polynomial Hamiltonian systems anti-symmetric under phase-space involutions, we generalize some results on the existence of Darboux polynomial and rational first integrals for "kinetic plus potential" systems to general systems.