The dynamics on three-dimensional strictly convex energy surfaces

• 成果类型: Article
• 署名作者: Hofer, H; Wysocki, K; Zehnder, E
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/120994
• 发表日期: 1998
• 页码: 197-289
• 关键词: pseudo-holomorphic-curves; pseudoholomorphic curves; seifert conjecture; symplectisations; 3-manifolds

摘要

We show that a Hamiltonian flow on a three-dimensional strictly convex energy surface S subset of R-4 possesses a global surface of section of disc type. It follows, in particular, that the number of its periodic orbits is either 2 or infinity, by a recent result of J. Franks on area-preserving homeomorphisms of an open annulus in the plane. The construction of this surface of section is based on partial differential equations of Cauchy-Riemann type for maps from punctured Riemann surfaces into R x S-3 equipped with special almost complex structures.