Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian - Hongying Zhu; Sumin Yang; Xiaochun Hu; Weihua Huang (Complexity)
In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at least 3 limit cycles emerging from the period annulus, and 3 limit cycles are near the boundaries.