Les difféomorphismes du cercle
Les difféomorphismes du cercle
Les systèmes simples sont disjoints de ceux qui sont infiniment divisibles et plongeables dans un flot
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.
Linear growth of the derivative for measure-preserving diffeomorphisms
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.