中国科学A辑(英文版)
中國科學A輯(英文版)
중국과학A집(영문판)
SCIENCE IN CHINA
2002年
8期
1038-1052
,共15页
Maslov-type index%iteration theory%star-shaped hypersurface%closed characteristics%non-degeneracy
In this paper, firstly we establish the relation theorem between the Maslov-type index and the index defined by C. Viterbo for star-shaped Hamiltonian systems. Then we extend the iteration formula of C. Viterbo for non-degenerate star-shaped Hamiltonian systems to the general case. Finally we prove that there exist at least two geometrically distinct closed characteristics on any non-degenerate star-shaped compact smooth hypersurface on R2n with n ＞ 1. Here we call a hypersurface non-degenerate, if all the closed characteristics on the given hypersurface together with all of their iterations are non-degenerate as periodic solutions of the corresponding Hamiltonian system. We also study the ellipticity of closed characteristics when n=2.
