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Methods of calculation of the Fomenko-Zieschang invariant. (English) Zbl 0744.58029
Topological classification of integrable systems, Adv. Sov. Math. 6, 147-183 (1991).
[For the entire collection see Zbl 0741.00026.]
A. T. Fomenko and H. Zieschang [Preprint Inst. Hautes Etudes Sci. /M/88/62, Bures-sur-Yvette (France)] introduced a topological invariant of Hamiltonian systems, \(I^*(Q,h)\) (where \(Q^ 3\) is the isoenergy surface), which classifies Hamiltonian systems up to topological equivalence. The central idea of this paper is to study Hamiltonian systems near singular points of the bifurcation diagrams, i.e., points at which there are bifurcations of the topological invariant \(I^*(Q,h)\).
As the author announced, the aim of the present paper is not to present a general theory; he only considers a number of examples which, in our opinion, are most interesting material in the theory.

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
57M50 General geometric structures on low-dimensional manifolds