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Centers of quasi-homogeneous polynomial planar systems. (English) Zbl 1238.34052
Summary: 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. We find 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.

34C05Location of integral curves, singular points, limit cycles (ODE)
34C07Theory of limit cycles of polynomial and analytic vector fields
37C99Smooth dynamical systems
Full Text: DOI
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