We consider an autonomous real polynomial Hamiltonian ordinary differential system. Sufficient conditions for the construction of additional first integrals on polynomial partial integrals and multiple polynomial partial integrals are obtained. Classes of autonomous polynomial Hamiltonian ordinary differential systems with first integrals which analytically expressed by multiple polynomial partial integrals are identified. Also we present examples that illustrate the theoretical results.
2010 Mathematics Subject Classification: 37J35, 37K10.
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