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Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems. (English) Zbl 0736.58022

On the base of developed Maslov-type index theory for paths in the symplectic groups the full classification of the linear Hamiltonian systems with continuous, periodic and symmetric coefficients is given. Using this theory the author obtains the existence theorems of multiple periodic solutions of asymptotically linear Hamiltonian systems. These results generalize the works of C. Conley and E. Zehnder, Commun. Pure Appl. Math. 37, 207-253 (1984; Zbl 0559.58019); M. L. Bertotti, Proc. Int. Conf., L’Aquila/Italy 1986, 135-145 (1987; Zbl 0645.34030) and K. C. Chang, Infinite Dimensional Morse Theory and Its Applications (1985; Zbl 0609.58001).

MSC:

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