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.
It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.
We construct a rank-one infinite measure preserving flow such that for each p > 0, the “diagonal” flow on the product space is ergodic.
Via the (C,F)-construction we produce a 2-fold simple mixing transformation which has uncountably many non-trivial proper factors and all of them are prime.
Page 1