Closed characteristics on compact convex hypersurfaces in R2n

• 成果类型: Article
• 署名作者: Long, YM; Zhu, CF
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062120
• 发表日期: 2002
• 页码: 317-368
• 关键词: maslov-type index; periodic-solutions; hamiltonian-systems; morse-theory; Orbits; Iteration; EXISTENCE; SURFACES; FORMULA; FLOW

摘要

For any given compact C-2 hypersurface Sigma in R-2n bounding a strictly convex set with nonempty interior, in this paper an invariant p(n)(Sigma) is defined and satisfies p(n)(Sigma) greater than or equal to [n/2] + 1, where [a] denotes the greatest integer which is not greater than a c R. The following results are proved in this paper. There always exist at least p(n)(Sigma) geometrically distinct closed characteristics on E. If all the geometrically distinct closed characteristics on E are nondegenerate, then p(n)(Sigma) greater than or equal to n. If the total number of geometrically distinct closed characteristics on E is finite, there exists at least an elliptic one among them, and there exist at least p(n)(Sigma) - 1 of them possessing irrational mean indices. If this total number is at most 2p(n)(Sigma) - 2, there exist at least two elliptic ones among them.