Limit-Cycle Replication via Chebyshev Pullbacks and a Quadratic Ceiling for Separable Schemes

Olimjon Eshkobilov, Shirali Kadyrov, Khudoyor Mamayusupov

Let \(H(n)\) denote the Hilbert number, i.e.\ the maximal number of limit cycles of planar polynomial vector fields of degree \(\le n\). A classical lower-bound mechanism for \(H(n…