Quasi-similarity, entropy and disjointness of ergodic systems

Answering Vershik's question we show that quasi-similarity does not conserve the entropy, proving quasi-similarity of all Bernoulli actions of a countable infinite group. We prove also the following generalization of Pinsker's theorem: the actions with zero Kirillov-Kushnirenko $P$-entropy and the actions with completely positive $P$-entropy are disjoint. Poisson suspensions are used as examples.Comment: in Russian languag

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