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 maps, the maximal automorphic factor is an odometer with an ergodic non-singular measure. We give conditions under which maps with absorbing Cantor sets 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.