Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841918 | Nonlinear Analysis: Theory, Methods & Applications | 2010 | 11 Pages |
Abstract
This paper deals with planar quasi-homogeneous polynomial vector fields, and addresses three major questions: the monodromy, the center–focus and the integrability problems. We characterize the monodromic planar quasi-homogeneous polynomial vector fields, and we give a condition to distinguish between a center and a focus in this case. Also, we provide conditions which characterize the integrability of quasi-homogeneous polynomial systems under non-resonance conditions. The results obtained allow us to analyse two monodromic planar systems with degenerate linear part: one of them with nilpotent linearization, and another one with null linear part.
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Authors
A. Algaba, E. Freire, E. Gamero, C. García,