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The Hamiltonian formalism and a many-valued analogue of Morse theory. (English. Russian original) Zbl 0571.58011
Russ. Math. Surv. 37, No. 5, 1-56 (1982); translation from Usp. Mat. Nauk 37, No. 5(227), 3-49 (1982).
The author surveys the earlier results (see the preceding reviews) and [Sov. Math., Dokl. 24, 222-226 (1981); translation from Dokl. Akad. Nauk SSSR 260, 31-35 (1981; Zbl 0505.58011)]. The Lyusternik-Shnirel’man-Morse theory is extended to many-valued functions and functionals (or closed \(\ell\)-forms). The methods are applied to construct a large collection of periodic orbits for the systems of Kirchhoff type.
Reviewer: T.Kawashima

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
37G99 Local and nonlocal bifurcation theory for dynamical systems
76B99 Incompressible inviscid fluids
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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