Multiple partial integrals of polynomial Hamiltonian systems
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2022-11-04 15:04
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517.925 (42)
Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (240)
SM ISO690:2012
PRANEVICH, Andrei, GRIN, Alexander, MUSAFIROV, Eduard. Multiple partial integrals of polynomial Hamiltonian systems. In: Acta et commentationes (Ştiinţe Exacte și ale Naturii), 2021, nr. 2(12), pp. 33-42. ISSN 2537-6284. DOI: https://doi.org/10.36120/2587-3644.v12i2.33-42
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Acta et commentationes (Ştiinţe Exacte și ale Naturii)
Numărul 2(12) / 2021 / ISSN 2537-6284 /ISSNe 2587-3644

Multiple partial integrals of polynomial Hamiltonian systems

Integrale particulare multiple ale sistemelor Hamiltoniene polinomiale

DOI: https://doi.org/10.36120/2587-3644.v12i2.33-42
CZU: 517.925
MSC 2010: 37J35, 37K10.

Pag. 33-42

Pranevich Andrei, Grin Alexander, Musafirov Eduard
 
Yanka Kupala State University of Grodno, Republic of Belarus
 
Disponibil în IBN: 10 februarie 2022


Rezumat

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

Cuvinte-cheie
Hamiltonian system, Darboux integrability, partial integral, multiplicity,

sistem Hamiltonian, integrabilitate Darboux, integrala particulara, multiplicitate