English

On a variant of Hilbert's 16th problem

Dynamical Systems 2024-11-07 v3

Abstract

We study the number of limit cycles that a planar polynomial vector field can have as a function of its number mm of monomials. We prove that the number of limit cycles increases at least quadratically with mm and we provide good lower bounds for m10m\leqslant10.

Cite

@article{arxiv.2405.04281,
  title  = {On a variant of Hilbert's 16th problem},
  author = {Armengol Gasull and Paulo Santana},
  journal= {arXiv preprint arXiv:2405.04281},
  year   = {2024}
}
R2 v1 2026-06-28T16:19:25.650Z