New Results in the Theory of Topological Classification of Integrable Systems: (Proceedings of the Steklov Institute of Mathematics)

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.

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