Analytic reducibility of nondegenerate centers: Cherkas systems
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems x˙ = y, y˙ = P0(x) + P1(x)y + P2(x)y2, where Pi(x) are polynomials of degree n, P0(0) = 0 and P'0(0) < 0. Computing the focal values we find the center conditions for such systems for degree 3, and using modular arithmetics for degree 4. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree n.
Grants:	Ministerio de Educación y Ciencia MTM2014-53703-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 Ministerio de Educación y Ciencia MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 316339
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Analytic integrability ; Center problem ; Polynomial Cherkas differential systems
Published in:	Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2016) , p. 1-10, ISSN 1417-3875

DOI: 10.14232/ejqtde.2016.1.49

Postprint 12 p, 363.9 KB

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