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Polymorphisms, Markov processes, quasisimilarity
1.  St. Petersburg Department of Steklov Institute of Mathematics, 27 Fontanka, St. Petersburg, 191023, Russian Federation 
The question is as follows: is it possible to have a quasisimilarity between a measurepreserving automorphism $T$ and a polymorphism $\Pi$ (that is not an automorphism)? In less definite terms: what kind of equivalence can exist between deterministic and random (Markov) dynamical systems? We give the answer: every nonmixing prime polymorphism is quasisimilar to an automorphism with positive entropy, and every $K$automorphism $T$ is quasisimilar to a polymorphism $\Pi$ that is a special random perturbation of the automorphism $T$.
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