Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Partial Integrals of Autonomous Polynomial Hamiltonian Ordinary Differential Systems

Author(s):

Andrei Pranevich

Department of Mathematics and Computer Science support for Economic Systems
Faculty of Economics and Management
Yanka Kupala State University of Grodno
Head of Department of Mathematics and Computer Science support for Economic Systems
Associate professor, Ph.D in Physics and Mathematics

pranevich@grsu.by

Abstract:

In this paper, we consider an autonomous polynomial Hamiltonian ordinary differential system. Sufficient criteria for the construction of first integrals on real polynomial partial integrals, multiple real polynomial partial integrals, conditional partial integrals, complex-valued polynomial partial integrals and multiple complex-valued polynomial partial integrals are obtained. Classes of autonomous polynomial Hamiltonian ordinary differential systems with first integrals which analytically expressed by real polynomial and conditional partial integrals, complex-valued polynomial and conditional partial integrals, real and complex-valued polynomial partial integrals are identified. The examples illustrating the obtained theoretical results are given.

Keywords

• first integral
• Hamiltonian system
• partial integral

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