NEW PROGRESS IN THE THEORY OF TRANSFORMATIONS WITH INVARIANT MEASURE

Abstract

CONTENTS Introduction § 1. The problem of isomorphism § 2. The work of Kolmogorov § 3. The entropy of an automorphism § 4. Properties of the entropy § 5. Computation of the entropy § 6. Automorphisms with zero entropy § 7. The entropy and the spectrum § 8. Kolmogorov automorphisms and automorphisms with completely positive entropy § 9. Exact endomorphisms § 10. Flows § 11. New problems References