Some lower bounds for \(H(n)\) in Hilbert's 16th problem (Q1431477)

The authors investigate perturbed \(Z_2\) (or \(Z_4)\)-equivariant planar Hamiltonian vector fields of degree \(n\), \(n= 2^k-1\) and \(n= 3\times 2^{k-1}\). They derive lower bounds for \(H(n)\) in Hilbert's 16th problem and determine configurations of the location of limit cycles. To this end, they use the bifurcation theory of planar dynamical systems and the quadruple transformation method.