A finiteness problem for one-dimensional maps

Abstract

We discuss the connection between the density of structurally stable maps in the space of unimodal maps of the interval, the finiteness of attractors and the nonexistence of wandering intervals. We show that in the space of unimodal maps having an eventually periodic flat critical point, there is a residual subset whose maps have infinitely many sinks. In this space there are also maps having a wandering interval.