Centers of quasi-homogeneous polynomial planar systems

2024/09/27 by Algaba, A., Fuentes, N., García, C.
#Dynamical Systems (math.DS) #F.2.2 #FOS: Mathematics #G.4 #I.2.7

paper · doi:10.48550/arxiv.2409.18774

Abstract

In this paper we determine the centers of quasi-homogeneous polynomial planar vector fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibility and the analytical integrability of each one of the above centers.Wefind polynomial centers which are neither orbitally reversible nor analytically integrable, this is a new scenario in respect to the one of non-degenerate and nilpotent centers.

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