This article is cited in 18 papers

Generic Mixing Transformations Are Rank $1$

A. I. Bashtanov

M. V. Lomonosov Moscow State University

Abstract: In 2007, S. V. Tikhonov introduced a complete metric on the space of mixing transformations. This metric generates a topology called the leash topology. Tikhonov posed the following problem: what conditions should be satisfied by a mixing transformation $T$ for its conjugacy class to be dense in the space of mixing transformations equipped with the leash topology. We show the conjugacy class to be dense for every mixing transformation $T$. As a corollary, we find that a generic mixing transformation is rank $1$.

Keywords: mixing transformation, probability space, conjugacy class, Tikhonov metric, leash topology.

UDC: 517.987.5+938.5

Received: 13.06.2012
Revised: 09.10.2012

DOI: 10.4213/mzm10157

 English version: Mathematical Notes, 2013, 93:2, 209–216

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