Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 108, pp. 1-6.

Title: Polynomial and rational integrability of polynomial 
       Hamiltonian systems

Authors: Jaume Llibre (Univ. Autonoma de Barcelona, Spain)
         Cristina Stoica (Wilfrid Laurier Univ., Waterloo,Ontario, Canada)
	 Claudia Valls (Univ. Tecnica de Lisboa, Portugal)

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.

Submitted January 26, 2012. Published June 26, 2012.
Math Subject Classifications: 37J35, 37K10.
Key Words: Polynomial Hamiltonian systems; polynomial first integrals;
           rational first integrals; Darboux polynomial.