Some Smooth Ergodic Systems

CONTENTS Introduction Lecture 1. The Maupertuis-Lagrange-Jacobi principle and reduction of a dynamical system to a geodesic flow. Some general properties of smooth dynamical systems Lecture 2. Y-systems Lecture 3. Verification of the Y-conditions for a geodesic flow on manifolds of negative curvature Lecture 4. Transversal foliations Lecture 5. Measurability and absolute continuity of transversal foliations for Y-systems Conclusion Appendix. G. A. Margulis, Y-flows on three-dimensional manifolds References