Monotone equivalence in ergodic theory

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 #x201C;words” arising from a coding of most trajectories by a finite partition. Also certain monotone invariants are defined and their properties discussed.