Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle

Abstract

It is known that perturbations from a Hamiltonian 2-saddle cycle F can produce limit cycles that are not covered by the Abelian integral, even when the Abelian integral is generic. These limit cycles are called alien limit cycles. In this paper, extending the results of [6] and [2], we investigate the number of alien limit cycles in generic multi-parameter rigid unfoldings of the Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation.