On the polynomial differential systems having polynomial first integrals
نویسندگان
چکیده
منابع مشابه
Polynomial First Integrals of Polynomial Differential Systems
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 integr...
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The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 · · ·f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . , p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in C2 h...
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We consider generalized Liénard polynomial differential systems of the form ˙ x = y, ˙ y = −g(x) − f (x) y, with f (x) and g(x) two polynomials satisfying deg(g) ≤ deg(f). In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In this letter, we give a direct and shorter proof of this result.
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2012
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2011.11.003