Azucena Caicedo, Jaume Llibre, and Claudio Vidal. Polynomial and Rational First Integrals for Non–Autonomous Polynomial Hamiltonian Systems. Dynamic Systems and Applications 29 (2020), No. 2, 239-247

https://doi.org/10.46719/dsa20202923

ABSTRACT.
Known results on the existence of polynomial and rational first integrals for autonomous
polynomial Hamiltonian systems are extended to non–autonomous polynomial Hamiltonian
systems invariant under an involution.

The key tool for proving these results is the existence of Darboux polynomials for the non–
autonomous polynomial Hamiltonian systems.

AMS (MOS) Subject Classification. 37J35, 37K10.