Integrable Geodesic Flows on Two-dimensional Surfaces

Preface. 1. Basic Notions. 2. Topology of Foliations Generated by Morse Functions on Two-Dimensional Surfaces. 3. Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom. 4. Liouville Equivalence of Integrable Systems with Two Degrees of Freedom. 5. Trajectory Classification of Integrable Systems with Two Degrees of Freedom. 6. Integrable Geodesic Flowson Two-Dimensional Surfaces. 7. Liouville Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces. 8. Trajectory Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces. 9. Maupertuis Principle and Geodesic Equivalence. 10. Euler Case in Rigid Body Dynamics and Jacob Problem About Geodesics on the Ellipsoid. Trajectory Isomorphism. References.