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. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials...

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Bibliographic Details
Authors: Giné, Jaume, Llibre, Jaume
Format: article
Status:Published version
Publication Date:2016
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/59108
Online Access:https://doi.org/10.14232/ejqtde.2016.1.49
http://hdl.handle.net/10459.1/59108
Access Level:Open access
Keyword:Center problem
Analytic integrability
Polynomial Cherkas differential systems
Description
Summary: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. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems 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.