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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


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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