A method for characterizing nilpotent centers

Giné, Jaume; Llibre, Jaume

doi:https://doi.org/10.1016/j.jmaa.2013.12.013

View/Open

Preprint (580.5Kb)

Issue date

2014

Author

Giné, Jaume

Llibre, Jaume

Suggested citation

Giné, Jaume; Llibre, Jaume; . (2014) . A method for characterizing nilpotent centers. https://doi.org/10.1016/j.jmaa.2013.12.013.

Abstract

To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the bifurcation of limit cycles from it or from its period annulus. We give an effective

algorithm in the search of necessary conditions for detecting nilpotent centers based in recent developments. Moreover we survey the last results on this problem and illustrate our approach by means of examples.