Generalized analytic integrability of a class of polynomial differential systems in C2
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China).)

Date:	2021
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) = (ax+ b) 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˙ = xf(y), y˙ = g(y), with f and g polynomials.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial systems ; Generalized analytic integrability ; Polynomial first integrals ; Residue
Published in:	Acta Applicandae Mathematicae, Vol. 173, Issue 1 (June 2021) , art. 1, ISSN 1572-9036

DOI: 10.1007/s10440-021-00407-4

Postprint 16 p, 686.2 KB

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