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New Results in the Theory of Topological Classification of Integrable Systems
Edited by: A. T. Fomenko
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Proceedings of the Steklov Institute of Mathematics
1995; 186 pp; softcover
Volume: 205
ISBN-10: 0-8218-0480-4
ISBN-13: 978-0-8218-0480-3
List Price: US$198 Member Price: US$158.40
Order Code: STEKLO/205

This collection contains new results in the topological classification of integrable Hamiltonian systems. Recently, this subject has been applied to interesting problems in geometry and topology, classical mechanics, mathematical physics, and computer geometry. This new stage of development of the theory is reflected in this collection.

Among the topics covered are: classification of some types of singularities of the moment map (including non-Bott types), computation of topological invariants for integrable systems describing various problems in mechanics and mathematical physics, construction of a theory of bordisms of integrable systems, and solution of some problems of symplectic topology arising naturally within this theory. A list of unsolved problems allows young mathematicians to become quickly involved in this active area of research.

Research mathematicians.

• S. S. Anisov -- On the topology of an integrable Hamiltonian system in the neighborhood of a degenerate one-dimensional trajectory
• E. V. Anoshkina -- Topological classification of an integrable case of Goryachev-Chaplygin type with generalized potential in the dynamics of a rigid body
• A. V. Bolsinov and A. T. Fomenko -- Unsolved problems in the theory of topological classification of integrable systems
• A. V. Bolsinov, A. T. Fomenko, and K. Chang -- Three types of bordisms of integrable systems with two degrees of freedom. Computation of bordism groups
• N. T. Zung -- Topological invariants of integrable geodesic flows on the higher-dimensional torus and sphere
• V. V. Kalashnikov -- Topological analysis of some systems of intramolecular dynamics of matter
• B. S. Kruglikov -- On the extension of the symplectic form and a pair of functions in involution from $$S^1\times I\times T^2$$
• B. S. Kruglikov -- Existence of a pair of additional Bott integrals for a resonance Hamiltonian system with two degrees of freedom
• O. E. Orel -- Investigation of a neighborhood of a degenerate one-dimensional orbit of the Poisson action of $$\mathbb R^2$$ in $$M^4$$
• A. A. Oshemkov -- Morse functions on two-dimensional surfaces. Encoding of singularities
• E. N. Selivanova -- The topology of the problem of three-point vortices
• I. A. Taĭmanov -- The topology of Riemannian manifolds with integrable geodesic flows
• P. Topalov -- Homological properties of labels of the Fomenko-Zieschang invariant
• V. V. Trofimov -- Generalized Maslov classes on the path space of a symplectic manifold
• Yu. N. Fedorov -- A generalized Poinsot interpretation of the motion of a multidimensional rigid body