Authors | _ |
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Journal | International Journal of Dynamical Systems and Differential Equations |
Page number | 247-266 |
Serial number | 12 |
Volume number | 3 |
Paper Type | Full Paper |
Published At | 2022 |
Journal Type | Typographic |
Journal Country | Switzerland |
Journal Index | Scopus |
Abstract
Abstract:We give a constructive approach to the degenerate center problem. First, we consider homogeneous polynomial systems and provide various conditions for which the origin is a center. Then, by using the Poincare coefficients in polar coordinate, we complete a rigorous computation such that the nonhomogeneous system perturbed by lower terms has an annular region surrounding the origin. This enables us to show that a degenerate center may be the limit of a linear center, a nilpotent singularity, and even a hyperbolic saddle point. Finally, we provide sufficient conditions such that the origin is a degenerate center for a nonhomogeneous system. The system may be of even degree, so we have degenerate centers of even degree, which are rare.
tags: center problem; degenerate center; Poincare map; polynomial