Moscow Mathematical Journal

Volume 18, Issue 3, July–September 2018 pp. 409–420.

On the Mechanisms for Producing Linear Type Centers in Polynomial Differential Systems

Authors: Jaume Giné (1) and Jaume Llibre (2)
Author institution:(1) Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain
(2) Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

Summary:

In this paper we study the mechanisms that provide linear type centers in the polynomial differential systems. These mechanisms are the algebraic reducibility and the Liouvillian integrability. We state a conjecture and some open questions. These mechanisms also explain all the known nilpotent and degenerate centers.

2010 Math. Subj. Class. Primary: 34C05; Secondary: 37C10.

Keywords: Center problem, Louville integrability, algebraic reducibility, polynomial differential systems.

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