Exactness and maximal automorphic factors of unimodal interval maps

We study exactness and maximal automorphic factors of C-3 unimodal maps of the interval. We show that for a large class of infinitely renormalizable m aps, the maximal automorphic factor is an odometer with an ergodic non-sing ular measure. We give conditions under which maps with absorbing Cantor set s have an irrational rotation on a circle as a maximal automorphic factor, as well as giving exact examples of this type. We also prove that every C-3 S-unimodal map with no attractor is exact with respect to Lebesgue measure . Additional results about measurable attractors in locally compact metric spaces are given.