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arXiv · 2405.04281

On a variant of Hilbert's 16th problem

Armengol Gasull·Paulo Santana
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Abstract

We study the number of limit cycles that a planar polynomial vector field can have as a function of its number $m$ of monomials. We prove that the number of limit cycles increases at least quadratically with $m$ and we provide good lower bounds for $m\leqslant10$.

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Armengol Gasull, Paulo Santana. 2024-05-07. On a variant of Hilbert's 16th problem. https://doi.org/10.1088/1361-6544/ad8c1b

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