A Poincare-Birkhoff theorem for tight Reeb flows on S3

• 成果类型: Article
• 署名作者: Hryniewicz, Umberto; Momin, Al; Salomao, Pedro A. S.
• 署名单位: Universidade Federal do Rio de Janeiro; Universidade de Sao Paulo
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0515-2
• 发表日期: 2015
• 页码: 333-422
• 关键词: pseudoholomorphic curves; contact homology; symplectisations; symplectizations; conjecture; points

摘要

We consider Reeb flows on the tight 3-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition then there exist infinitely many periodic trajectories distinguished by their linking numbers with the components of the link. This result admits a natural comparison to the Poincar,-Birkhoff theorem on area-preserving annulus homeomorphisms. An analogous theorem holds on and applies to geodesic flows of Finsler metrics on S-3.