# American Institute of Mathematical Sciences

November  2013, 12(6): 2797-2809. doi: 10.3934/cpaa.2013.12.2797

## Analytic integrability for some degenerate planar systems

 1 Department of Mathematics, University of Huelva, 21071-Huelva 2 Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69. 25001. Lleida.

Received  October 2012 Revised  February 2013 Published  May 2013

In the present paper we characterize the analytic integrability around the origin of a family of degenerate differential systems. Moreover, we study the analytic integrability of some degenerate systems through the orbital reversibility and from the existence of a Lie's symmetry for these systems. The results obtained for this family are similar to the results obtained when we characterize the analytic integrability of non-degenerate and nilpotent systems. The obtained results can be applied to compute the analytic integrable systems of any particular family of degenerate systems studied.
Citation: Antonio Algaba, Cristóbal García, Jaume Giné. Analytic integrability for some degenerate planar systems. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2797-2809. doi: 10.3934/cpaa.2013.12.2797
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