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arXiv · 2407.13465

A note on Hilbert 16th Problem

Armengol Gasull·Paulo Santana
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Abstract

Let $\mathcal{H}(n)$ be the maximum number of limit cycles that a planar polynomial vector field of degree $n$ can have. In this paper we prove that $\mathcal{H}(n)$ is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.

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Armengol Gasull, Paulo Santana. 2024-07-18. A note on Hilbert 16th Problem. https://doi.org/10.1090/proc/17116

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