次二次Hamilton系统的对偶Morse指标及其闭特征的稳定性

Dual Morse Index for Subquadratic Hamiltonian Systems and the Stability of the Closed Characteristics

本文通过Ｇｅｌｅｒｋｉｎ逼近方法，在没有任何凸的条件下，研究了次二次Ｈａｍｉｌ－ｔｏｎ系统的ｋ对偶Ｍｏｒｓｅ指标理论．作为应用，在本文研究了Ｒ２ｎ中的凸超曲面上的闭特征的稳定性，证明了在一个较宽松的夹条件下，这类超曲面上至少有一条椭圆闭特征．

In this paper, by using the direct variational and the Gelerkin approximation methods, we study the dual Morse k-index theory of subquadratic Hamiltonian systems without conexity. As an application, we study the stability of closed characteristics on the strictly convex C2 conmpact hypersurface in R2n. We prove that under a relaxed pinched condition, there exists a strictly elliptic characteristic on .