Note on Subharmonic Solutions of a Hamiltonian Vector Field.
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A forced oscillation problem for a Hamiltonian equation on a torus is studied. If the dimension of the torus is equal to 2n, and if the period of the time dependent Hamiltonian equation is equal to 1, it has been shown in another document, that there are at least 2n1 periodic solutions having period 1. In this paper it is shown, that, under an additional, necessary nondegeneracy condition such an equation possesses a periodic solution having minimal period T, for every sufficiently large prime number T. The proof uses the classical variational approach. It is based on the Morse theory for periodic solutions developed in 5 which relates the winding number of a periodic solution to its Morse index and on an iteration formula for the winding number. Author
- Numerical Mathematics