Saddle-nodes and period-doublings of Smalehorseshoes: a case study near resonanthomoclinic bellows

摘要

In unfoldings of resonant homoclinic bellows interesting bifurcation phe-nomena occur: two suspensed Smale horseshoes can collide and disappearin saddle-node bifurcations (all periodic orbits disappear through saddle-nodebifurcations, there are no other bifurcations of periodic orbits), or a suspendedhorseshoe can go through saddle-node and period-doubling bifurcations of theperiodic orbits in it to create an additional "doubled horseshoe".