Regular or stochastic dynamics in families of higher-degree unimodal maps

Abstract

AbstractWe construct a lamination of the space of unimodal maps with critical points of fixed degree $d\geq 2$ by the hybrid classes. The structure of the lamination yields a partition of the parameter space for one-parameter real analytic families of unimodal maps and allows us to transfer a priori bounds in the phase space to the parameter space. This implies that almost every map in such a family is either regular or stochastic.