On a variant of Hilbert's 16th problem

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 $m⩽10$.

References in corpus (1)

• Generalized Mass-Action Systems and Positive Solutions of Polynomial Equations with Real and Symbolic Exponents