Polynomial and rational integrability of polynomial Hamiltonian systems

Abstract

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.

Keywords

• Polynomial Hamiltonian systems
• polynomial first integrals
• rational first integrals
• Darboux polynomial