@article{10272/25456,
year = {2012},
month = {6},
url = {https://hdl.handle.net/10272/25456},
abstract = {We characterize the nilpotent systems whose lowest degree quasi-homogeneous term is (y,σxn)T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the systems with formal inverse integrating factor are formally orbital equivalent to (x˙,y˙)T=(y,xn)T. In the case n odd, we give a formal normal form that characterizes them. As a consequence, we give the link among the existence of formal inverse integrating factor, center problem and integrability of the considered systems.},
organization = {This work has been partially supported by Ministerio de Ciencia y Tecnología, Plan Nacional I+D+I
co-financed with FEDER funds, in the frame of the projects
MTM2007-64193 and MTM2010-20907-C02-02, and by 
Consejería de Educación y Ciencia de la Junta de
Andalucía (FQM-276 and P08-FQM-03770).},
publisher = {Elsevier},
title = {Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems},
doi = {10.1016/j.chaos.2012.02.016},
author = {Algaba Durán, Antonio and García García, Cristóbal and Reyes Columé, Manuel},
}