Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation T which is conjugate to T². 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 T² and whose rank is finite and greater than n.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-1-4,
author = {Alexandre I. Danilenko},
title = {Weakly mixing rank-one transformations conjugate to their squares},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {75-93},
zbl = {1143.37004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-1-4}
}
Alexandre I. Danilenko. Weakly mixing rank-one transformations conjugate to their squares. Studia Mathematica, Tome 187 (2008) pp. 75-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-1-4/