A NOTE ON HILBERT 16TH PROBLEM - Gasull, Armengol; Santana, Paulo [UNESP] (American Mathematical Society (AMS), 2025)
Let 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 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.
Keywords: Hilbert 16th problem; limit cycles; structurally stable vector fields