Finite energy foliations of tight three-spheres and Hamiltonian dynamics

• 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: 10.4007/annals.2003.157.125
• 发表日期: 2003
• 页码: 125-255
• 关键词: pseudo-holomorphic-curves; pseudoholomorphic curves; weinstein conjecture; 3-manifolds; symplectizations; symplectisations; MANIFOLDS; index; FLOW

摘要

Surfaces of sections are a classical tool in the study of 3-dimensional dynamical systems. Their use goes back to the work of Poincare and Birkhoff. In the present paper we give a natural generalization of this concept by constructing a system of transversal sections in the complement of finitely many distinguished periodic solutions. Such a system is established for nondegenerate Reeb flows on the tight 3-sphere by means of pseudoholomorphic curves. The applications cover the nondegenerate geodesic flows on T1S2 = RP3 via its double covering S-3, and also nondegenerate Hamiltonian systems in R-4 restricted to sphere-like energy surfaces of contact type.