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.

Se considera sistemele autonome, reale, polinomiale s, i Hamiltoniane de ecuatii diferentiale ordinare. Sunt obtinute unele conditii suficiente de construire a integralelor prime pe baza integralelor particulare polinomiale simple si multiple si sunt identificate sistemele diferentiale ce au astfel de integrale prime. Rezultatele teoretice sunt ilustrate prin exempl