Abstract
Generic (i.e., forming an everywhere dense massive subset) classes of Markov operators in the space L 2 (X, µ) with a finite continuous measure are con- sidered. In a canonical way, each Markov operator is associated with a multivalued measure-preserving transformation (i.e., a polymorphism), and also with a station- ary Markov chain; therefore, one can also talk of generic polymorphisms and generic Markov chains. Not only had the generic nature of the properties discussed in the paper been unclear before this research, but even the very existence of Markov op- erators that enjoy these properties in full or partly was known. The most important result is that the class of totally nondeterministic nonmixing operators is generic. A number of problems is posed; there is some hope that generic Markov operators will find applications in various fields, including statistical hydrodynamics.
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