This article is cited in 8 papers

On the mechanisms for producing linear type centers in polynomial differential systems

Jaume Gine^a, Jaume Llibre<sup>b

a</sup> Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain
^b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

Abstract: 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.

Key words and phrases: center problem, Louville integrability, algebraic reducibility, polynomial differential systems.

MSC: Primary 34C05; Secondary 37C10

Language: English

DOI: 10.17323/1609-4514-2018-18-3-409-420

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