On a variant of Hilbert's 16th problem - Gasull, Armengol; Santana, Paulo [UNESP] (IOP Publishing, 2024)
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 ≤ 10.
Keywords: Abelian integrals; Hilbert 16th problem; limit cycles