A Poincare-Birkhoff theorem for tight Reeb flows on S-3

Autor(es)

Hryniewicz, Umberto ^[1] ; Momin, Al ^[2] ; Salomao, Pedro A. S. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Rio de Janeiro, Dept Matemat Aplicada, BR-21941909 Rio De Janeiro, RJ - Brazil

^[2] Evermight, Toronto, ON - Canada

^[3] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INVENTIONES MATHEMATICAE; v. 199, n. 2, p. 333-422, FEB 2015.
• Citações Web of Science: 12

Resumo

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. (AU)

• Processo FAPESP: 11/16265-8 - Dinâmica em baixas dimensões
• Beneficiário: Edson Vargas
• Modalidade de apoio: Auxílio à Pesquisa - Temático