Measure-preserving rank one transformations

V. V. Ryzhikov

Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 81 (2020) no. 2, pp. 281-318.

Résumé

Rank 1 transformations serve as a source of examples in ergodic theory showing a variety of algebraic, asymptotic, and spectral properties of dynamical systems. The properties of a rank one transformation are closely related to the structure of the semigroup of weak limits of its powers. In this vein, known and new constructions of transformations are studied.

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