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Keywords:
ergodic measure preserving transformation; type $\text{III}_0$ cocycle; T-set; cocycle with unbounded gaps
ergodic measure preserving transformation; type $\text{III}_0$ cocycle; T-set; cocycle with unbounded gaps
Summary:
An example of type III$_0$ cocycle without unbounded gaps of an ergodic probability measure preserving transformation will be shown.
References:
[1] Hamachi T., Oka Y., Osikawa M.: A classification of ergodic non-singular transformation groups. Mem. Fac. Sci. Kyushu Univ. 18 (1974), 113-133. MR 0432859 | Zbl 0293.28011
[2] Hamachi T., Oka Y., Osikawa M.: Flows associated with ergodic non-singular transformation groups. Publ. RIMS Kyoto Univ. 11 (1975), 31-50. MR 0390172 | Zbl 0316.28007
[3] Lemańczyk M.: Private communications.
[4] Lemańczyk M.: Analytic nonregular cocycles over irrational rotations. Comment. Math. Univ. Carolinae 36.4 (1995), 727-735. MR 1378694
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