Geodesic
Generic Mixing Transformations Are Rank~$1$
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 163-171

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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, Tikhonov metric, leash topology.
Mots-clés : conjugacy class 
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     author = {A. I. Bashtanov},
     title = {Generic {Mixing} {Transformations} {Are} {Rank~}$1$},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {93},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a0/}
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A. I. Bashtanov. Generic Mixing Transformations Are Rank~$1$. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 163-171. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a0/