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On new spectral multiplicities for ergodic maps

100%
Danilenko A.
Studia Mathematica
|
2010
|
tom 197
|
nr 1
57-68
EN
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.
2
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Weakly mixing rank-one transformations conjugate to their squares

100%
Danilenko A.
Studia Mathematica
|
2008
|
tom 187
|
nr 1
75-93
EN
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.
3
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Infinite measure preserving flows with infinite ergodic index

63%
Danilenko A., Solomko A.
Colloquium Mathematicum
|
2009
|
tom 115
|
nr 1
13-19
EN
We construct a rank-one infinite measure preserving flow $(T_r)_{r∈ ℝ}$ such that for each p > 0, the "diagonal" flow $(T_r × ⋯ × T_r)_{r∈ ℝ} (p times)$ on the product space is ergodic.
4
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Simple mixing actions with uncountably many prime factors

63%
Danilenko A., Solomko A.
Colloquium Mathematicum
|
2015
|
tom 139
|
nr 1
37-54
EN
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.
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