Polynomial and rational integrability of polynomial Hamiltonian systems - Jaume Llibre; Cristina Stoica; Claudia Valls (Electronic Journal of Differential Equations, 2012)
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.