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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Hryniewicz, Umberto [1] ; Momin, Al [2] ; Salomao, Pedro A. S. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: INVENTIONES MATHEMATICAE; v. 199, n. 2, p. 333-422, FEB 2015.
Web of Science Citations: 12
Abstract

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)

FAPESP's process: 11/16265-8 - Low dimensional dynamics
Grantee:Edson Vargas
Support Opportunities: Research Projects - Thematic Grants