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We show that expanding toral endomorphisms, together with their respectiveLebesgue measure are isomorphic to 1-sided Bernoulli shifts. This result isthen extended to smooth perturbations of expanding toral endomorphisms,together with their respective measures of maximal entropy. Also we study groupextensions of expanding toral endomorphisms and show that under certain, nottoo restrictive conditions on the extension cocycle, these skew products are1-sided Bernoulli as well.

Isomorphism classes for certain expanding maps and their group extensions