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In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system . The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most and at least limit cycles emerging from the period annulus, and limit cycles are near the boundaries.

Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian