Cyclicity of a class of polynomial nilpotent center singularities

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2016-04-01
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García, I. A. (Isaac A.)García, I. A. (Isaac A.) - ORCID ID
Shafer, Douglas S.
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In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + 1}(x,y)$, $\dot y = Q_{2m + 1}(x,y)$, where $P_{2m+1}$ and $Q_{2m+1}$ are homogeneous polynomials of degree $2m + 1$ in $x$ and $y$. We use the method to obtain an upper bound (which is sharp in this case) on the cyclicity of all centers in the cubic family and all centers in a broad subclass in the quintic family.
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Discrete and Continuous Dynamical Systems Series A, 2016, vol. 36, núm. 5, p. 2497-2520