The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems

Dong, Di; Long, Yiming

doi:10.1090/S0002-9947-97-01718-2

The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
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by Di Dong and Yiming Long PDF

Trans. Amer. Math. Soc. 349 (1997), 2619-2661 Request permission

Abstract:

In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous, periodic, and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems, and unify known results under various convexity conditions.

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