The Hamiltonian formalism and a many-valued analogue of Morse theory. (English. Russian original) Zbl 0571.58011

Novikov, S. P.

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

Keywords:

periodic orbits; Lyusternik-Shnirel’man-Morse theory; integrals of closed l-forms; Kirchhoff problem

Citations:

Zbl 0571.58009; Zbl 0571.58010; Zbl 0505.58011