The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems |
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| Authors: | Di Dong Yiming Long |
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| Institution: | Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China ; Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China |
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| 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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| Keywords: | Normal form of a symplectic matrix perturbation of eigenvalues symplectic path Maslov-type index iteration formula minimal period Hamiltonian systems |
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