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We prove that simple transformations are disjoint from those which are infinitely divisible and embeddable in a flow. This is a reinforcement of a previous result of A. del Junco and M. Lemańczyk [1] who showed that simple transformations are disjoint from Gaussian processes.
We consider measure-preserving diffeomorphisms of the torus with zero entropy. We prove that every ergodic -diffeomorphism with linear growth of the derivative is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle -cocycle. We also show that for no positive β ≠ 1 does there exist an ergodic -diffeomorphism whose derivative has polynomial growth with degree β.
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