Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems

A. Algaba, C. García and M. Reyes

Chaos, Solitons & Fractals, 2012, vol. 45, issue 6, 869-878

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:6:p:869-878

DOI: 10.1016/j.chaos.2012.02.016

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