Fomenko invariants in the theory of integrable Hamiltonian systems

Abstract

Contents Introduction The case of one degree of freedom, Morse functions on two-dimensional surfaces, atoms, gradient-like flows Singularities of codimension one The case of two degrees of freedom, isoenergetic surfaces, molecules Circular molecules and the Fomenko conjecture Non-degenerate singularities in the case of many degrees of freedom. The topological decomposition theorem Orbital classification of integrable Hamiltonian systems The Jacobi problem of geodesies on an ellipsoid and the Euler case in rigid body dynamicsBibliography