Abstract:
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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