Analytic reducibility of nondegenerate centers: Cherkas systems

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 po...

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Detalles Bibliográficos
Autores: Giné, Jaume|||0000-0001-7109-2553, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169493
Acceso en línea:https://ddd.uab.cat/record/169493
https://dx.doi.org/urn:doi:10.14232/ejqtde.2016.1.49
Access Level:acceso abierto
Palabra clave:Analytic integrability
Center problem
Polynomial Cherkas differential systems
Descripción
Sumario: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.