Monotone equivalence in ergodic theory

A. B. Katok

Izvestiya. Mathematics , Tome 11 (1977) no. 1, pp. 99-146.

Résumé

A class of monotonely equivalent automorphisms (standard automorphisms), which includes all ergodic automorphisms with discrete spectrum and most of the well-known examples of automorphisms with zero entropy, is studied. The basic results are two necessary and sufficient conditions for standardness: the first in terms of periodic approximation and the second in terms of the asymptotic properties of “words” arising from a coding of most trajectories by a finite partition. Also certain monotone invariants are defined and their properties discussed. Bibliography: 36 titles.

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