A complete metric in the set of mixing transformations

S. V. Tikhonov

Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 575-596

Résumé

A metric in the set of mixing measure-preserving transformations is introduced making of it a complete separable metric space. Dense and massive subsets of this space are investigated. A generic mixing transformation is proved to have simple singular spectrum and to be a mixing of arbitrary order; all its powers are disjoint. The convolution powers of the maximal spectral type for such transformations are mutually singular if the ratio of the corresponding exponents is greater than 2. It is shown that the conjugates of a generic mixing transformation are dense, as are also the conjugates of an arbitrary fixed Cartesian product. Bibliography: 28 titles.

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