Weakly mixing rank-one transformations conjugate to their squares
Volume 187 / 2008
Studia Mathematica 187 (2008), 75-93
MSC: Primary 37A40; Secondary 37A15, 37A20, 37A30.
DOI: 10.4064/sm187-1-4
Abstract
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 $n$.
