Isomorphism classes for certain expanding maps and their group extensions

Abstract

We show that expanding toral endomorphisms, together with their respective Lebesgue measure are isomorphic to 1-sided Bernoulli shifts. This result is then extended to smooth perturbations of expanding toral endomorphisms, together with their respective measures of maximal entropy. Also we study group extensions of expanding toral endomorphisms and show that under certain, not too restrictive conditions on the extension cocycle, these skew products are 1-sided Bernoulli as well.