PERIODIC-ORBITS FOR INTERVAL MAPS WITH SHARP CUSPS

We study families of unimodal interval maps having a sharp cusp at a critical point. We describe bifurcations and distribution of periodic orbits. Period adding for attracting periodic orbits is observed, that is, period k is followed by k + 1, etc. Coexistence of attractors of successive periods, as well as of an attracting fixed point and chaos occurs. Periodic orbits of various periods are grouped into bunches and occupy a relatively small part of the space.