Geodesic
Mixing on Sequences
Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 339-352

Voir la notice de l'article provenant de la source Cambridge University Press

Our aim is to study the mixing sequences of a weak mixing transformation. An ergodic measure preserving transformation is weak mixing if and only if for each pair of sets there exists a sequence of density one on which the transformation mixes the sets [9]. An unpublished result of S. Kakutani implies there actually exists a single sequence of density one on which the transformation is mixing for all sets (see Section 3). This result motivated the general définition of a transformation being mixing on a sequence, as well as mixing of higher order on a sequence. Given a weak mixing transformation, there exist sequences along which it is mixing of all degrees. In particular, this is the case for an eventually independent sequence [7].In Section 3 it will be shown that if T is weak mixing but not mixing, then a sequence on which T is two-mixing must have upper density zero. 
Mixing on Sequences. Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 339-352. doi: 10.4153/CJM-1983-019-2
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