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- Title
Generalized Analytic Integrability of a Class of Polynomial Differential Systems in C2.
- Authors
Llibre, Jaume; Tian, Yuzhou
- Abstract
This paper study the type of integrability of differential systems with separable variables x ˙ = h (x) f (y) , y ˙ = g (y) , where h , f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. Moreover we characterize the polynomial integrability of all such systems. In the particular case h (x) = (a x + b) m we provide necessary and sufficient conditions in order that this subclass of systems has a generalized analytic first integral. These results extend known results from Giné et al. (Discrete Contin. Dyn. Syst. 33:4531–4547, 2013) and Llibre and Valls (Discrete Contin. Dyn. Syst., Ser. B 20:2657–2661, 2015). Such differential systems of separable variables are important due to the fact that after a blow-up change of variables any planar quasi-homogeneous polynomial differential system can be transformed into a special differential system of separable variables x ˙ = x f (y) , y ˙ = g (y) , with f and g polynomials.
- Subjects
POLYNOMIALS; HOMOGENEOUS polynomials
- Publication
Acta Applicandae Mathematicae, 2021, Vol 173, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-021-00407-4