Öcenterlineä MEMOIRS ON INTEGRABLE SYSTEMSü Ömedskip Öcenterlineä TABLE OF CONTENTSü Öbigskip Chapter I. CLASSICAL MECHANICS AND LIE GROUPS. 1.1. Momentum theorem 1.2. Multi-dimensional dynamics 1.3.

The Euler--PoincarÖè equations Öbigskip Chapter II. SYSTEMS WITH AN INVARIANT MEASURE. 2.1. Integral invariants 2.2. Integrability 2.3.

The Kowalewski--Lyapunov method 2.4. Examples of systems with an invariant measure 2.5 Systems with an invariant measure on Lie groups Öbigskip Chapter III. INTEGRABLE SYSTEMS, LAX PAIRS AND CONFOCAL QUADRICS 3.1. Geometry 3.2.

Lax pairs and hierarchies of integrable Hamiltonian systems 3.3. Hierarchy of the Frahm--Manakov and Clebsch--Perelomov systems 3.4. Hierarchy of the Steklov--Lyapunov--Rubanovsky systems 3.5. The FMCP hierarchy and common tangent linear spaces of confocal quadrics 3.6.

Complete KÖ"otters solution for the Clebsch case 3.7. Integrable nonholonomic systems on $so(n)$ 3.8. The Steklov--Lyapunov systems and pencils of lines Öbigskip Chapter IV. EXPLICIT SOLUTIONS 4.1. Abelian tori and Jacobians 4.

2. Theta-functional solutions 4.3. Solutions in generalized theta-functions. Öbigskip References Index.