Translated by Semenov-Tian-Shansky, M.A., Reyman, A.G.
1994, VII, 344 p.
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0. A nonholonomic manifold is a smooth manifold equipped with a smooth distribution. This distribution is in general nonintegrable. The term 'holonomic' is due to Hertz and means 'universal', 'integral', 'integrable' (literally, oA.o
Contents: Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems by A.M. Vershik, V.Ya. Gershkovich.- Integrable Systems and Infinite Dimensional Lie Algebras by M.A. Olshanetsky, M.A. Perelomov.- Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems by A.G. Reyman, M.A. Semenov-Tian-Shansky.- Quantization of Open Toda Lattices by M.A. Semenov-Tian-Shansky.- Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras by V.V. Trofimov, A.T. Fomenko.