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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 482305, 10 pages
http://dx.doi.org/10.1155/2013/482305
Research Article

On the Formal Integrability Problem for Planar Differential Systems

1Departamento de Matemàticas, Facultad de Ciencias, Avda. Tres de Marzo s/n, 21071 Huelva, Spain
2Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia, Spain

Received 15 November 2012; Accepted 28 January 2013

Academic Editor: Sung Guen Kim

Copyright © 2013 Antonio Algaba et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in , and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.