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arXiv · 2409.18774

Centers of quasi-homogeneous polynomial planar systems

A. Algaba·N. Fuentes·C. García
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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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A. Algaba, N. Fuentes, C. García. 2024-09-27. Centers of quasi-homogeneous polynomial planar systems. https://arxiv.org/abs/2409.18774

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