Higher dimensional expanding maps and toral extensions (Q2845422)

In the study of automorphisms and endomorphisms of Lebesgue spaces, the results and techniques are quite different since the negative orbits of some point are not unique. However, in some special cases, such as linear expanding endomorphisms on tori, one can get similar results.NEWLINENEWLINEIn the paper under review, the author shows that expanding endomorphisms on tori are 1-sided Bernoulli with respect to their corresponding measure of maximal entropy. This applies in particular to expanding linear toral endomorphisms and their smooth perturbations. Then the author studies toral extensions of expanding toral endomorphisms, in particular probabilistic systems on skew products, and proved that under certain conditions, these skew products are 1-sided Bernoulli.