Bifurcation set and distribution of limit cycles for a class of seven-order Hamiltonian system with fifteen-order perturbed terms

A class of seven-order planar Z(7)-equivariant Hamiltonian system with rota tion symmetry and the fifteen-order perturbed term are investigated. By usi ng the bifurcation theory, qualitative method, detection function and numer ical simulations, we obtain: (1) explicit formulas for the global and local bifurcations of the flow; (2) 15 limit cycles with distribution 7C(1)(2) s ubset of C-27(1). These results in this paper are useful for the study of t he weakened Hilbert 16th problem. (C) 2001 Published by Elsevier Science Lt d.