On the centers of the weight-homogeneous polynomial vector fields on the plane
Jaume Llibre, Claudio Pessoa
TL;DR
This paper classifies all the centers of planar weight-homogeneous polynomial vector fields for weights 1 through 4, providing a comprehensive understanding of their center configurations.
Contribution
It offers a complete classification of centers for weight-homogeneous polynomial vector fields on the plane for specific weights, filling a gap in the existing literature.
Findings
Complete classification for weights 1 to 4
Identification of conditions for centers
Extension of previous classifications
Abstract
We classify all the centers of a planar weight-homogeneous polynomial vector field of weight degree 1, 2, 3 and 4.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Differential Geometry Research · Nonlinear Waves and Solitons