Journal of Modern Dynamics (JMD)

A note on Reeb dynamics on the tight 3-sphere

Pages: 597 - 613, Issue 4, October 2007      doi:10.3934/jmd.2007.1.597

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Frédéric Bourgeois - Département de Mathématique, Université Libre de Bruxelles CP 218, Boulevard du Triomphe, 1050 Bruxelles, Belgium (email)
Kai Cieliebak - Mathematisches Institut der LMU München, Theresienstr. 39, 80333 München, Germany (email)
Tobias Ekholm - Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden (email)

Abstract: We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable irrational ellipsoid in 4-space.

Keywords:  Reeb dynamics, contact homology, periodic orbit.
Mathematics Subject Classification:  Primary: 57R58; Secondary: 57R17, 35B10.

Received: March 2007;      Revised: July 2007;      Available Online: July 2007.