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Polynomial and rational integrability of polynomial Hamiltonian systemsKeywords: Polynomial Hamiltonian systems , polynomial first integrals , rational first integrals , Darboux polynomial 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.
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