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Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems. (English. Russian original) Zbl 0673.58023

Math. USSR, Sb. 63, No. 2, 319-336 (1989); translation from Mat. Sb., Nov. Ser. 135(177), No. 3, 325-345 (1988).
A connection between a topological classification of 3-dimensional manifolds and a symplectic topology of integrable Hamiltonian systems is discovered and studied. In particular an equivalence of a class (S) of 3- dimensional closed compact manifolds with a smooth function whose critical point set consists of nondegenerate circles, a class (H) of irreducible closed isoenergetic manifolds of integrable Hamiltonian systems and a class of irreducible closed manifolds possessing circular Morse function is proved. An explicit condition for the existence of minimal circular Morse function on connected closed manifold \(M^ n\), \(n\geq 6\) is given.
Reviewer: E.D.Belokolos

MSC:

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.)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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