Integrable Hamiltonian Systems

Basic Notions. The Topology of Foliations on Two-Dimensional Surfaces Generated by Morse Functions. Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom. Liouville Equivbalence of Integrable Systems with Two Degrees of Freedom. Orbital Classification of Integrable Systems with Two Degrees of Freedom. Classification of Hamiltonian Flows on Two-Dimensional Surfaces up to Topological Conjugacy. Smooth Conjugacy of Hamiltonian Flows on Two-Dimensional Surfaces. Orbital Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second Step. Liouville Classification of Integrable Systems with Two Degrees of Freedom in Four-Dimensional Neighborhoods of Singular Points. Methods of Calculation of Topological Invariants of Integrable Hamiltonian Systems. Integrable Geodesic Flows on Two-Dimensional Surfaces. Liouville Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces. Orbital Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces. The Topology of Liouville Foliations in Classical Integrable Cases in Rigid Body Dynamics. Maupertuis Principle and Geodesic Equivalence.