In this Letter we study some aspects of the relationship between the existence of Darboux polynomials and additional polynomial first integrals in natural polynomial Hamiltonian systems with a finite number of degrees of freedom. More precisely, first we improve results of the paper of Maciejewski and Przybylska [A.J. Maciejewski, M. Przybylska, Phys. Lett. A 326 (2004) 219]; and after we answer two open questions presented in that paper. © 2010 Elsevier B.V.
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Publication status||Published - 25 Oct 2010|
- Darboux polynomial
- Hamiltonian system
- Polynomial first integral
- Polynomial potential