Polynomial First Integrals of Polynomial Differential Systems
نویسندگان
چکیده
In this paper we shall primarily study polynomial integrability of the differential system ẋ = −y + Pn(x, y), ẏ = x + Qn(x, y), n = 2, 3, where Pn and Qn are homogeneous polynomials of degree n. By taking various yet very elementary ways, we not only straightforwardly find the necessary and sufficient integrability conditions but also explicitly present the corresponding polynomial first integrals. Moreover, we give a unified description about the polynomial integrability conditions in terms of some invariance.
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تاریخ انتشار 2004