Nonholonomic systems provide an important class of mechanical control systems. One
reason for this importance is that nonintegrability is essential to both the mechanics and the …

Abstract Contents Introduction § 0. Definitions, notation, and basic facts § 1. The universal 1-
form. Lagrangian manifolds § 2. Fields and 1-forms on Φ § 3. Poisson brackets § 4 …

In this paper we shall show that the equations of motion of a solid, and also Liouville's
method of integration of Hamiltonian systems, appear in a natural manner when we study …

Abstract CONTENTS Introduction § 1. Necessary facts from symplectic geometry § 2.
Different versions of non-commutative integration in the Liouville sense § 3. Sectional …

§ 1. Introduction. This paper deals with the complete integrability of the equations of motion
of a free «-dimensional rigid body about a fixed point. The Euler vector fields on a Lie …

This paper deals with the integration of a periodic problem for nonlinear systems associated
with matrix linear differential operators of first order by methods that generalize the methods …

The universal enveloping algebra of any simple Lie algebra g contains a family of
commutative subalgebras, called the quantum shift of argument subalgebras. We prove that …

Moment maps are defined from the space of rank-r deformations of a fixed nxn matrix A to
the duals (g1 (r)^+)^*,(g1 (n)^+)^* of the positive half of the loop algebras g1 (r), g1 (n) …

We discuss the relationship between the representation of an integrable system as an LA-
pair with a spectral parameter and the existence of two compatible Hamiltonian …

This article describes new results obtained in the theory of symmetries and singularities of
integrable Hamiltonian systems, developed in recent years by the Fomenko school in …