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## Weakly mixing rank-one transformations conjugate to their squares

### Tom 187 / 2008

Studia Mathematica 187 (2008), 75-93 MSC: Primary 37A40; Secondary 37A15, 37A20, 37A30. DOI: 10.4064/sm187-1-4

#### Streszczenie

Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation $T$ which is conjugate to $T^2$. Moreover, it is proved that for each odd $q$, there is such a $T$ commuting with a transformation of order $q$. For any $n$, we show the existence of a weakly mixing $T$ conjugate to $T^2$ and whose rank is finite and greater than $n$.

#### Autorzy

• Alexandre I. DanilenkoMax Planck Institute for Mathematics
Vivatsgasse 7
Bonn, 53111, Germany
and
Institute for Low Temperature Physics & Engineering
of Ukrainian National Academy of Sciences
47 Lenin Ave.
Kharkov, 61164, Ukraine
e-mail

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