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Moments and lower bounds in the farfield of solutions to quasigeostrophic flows
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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