Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4

In the analytic case we prove the conjecture of Maciejewski and Przybylska [J. Math. Phys.46(6), 062901 (2005)] regarding Hamiltonian systems with a homogeneous polynomial potential of degree 4. The proof of the conjecture completes the characterization of all the analytic integrable Hamiltonian system with a homogeneous polynomial potential of degree 4. © 2011 American Institute of Physics.