A note on Reeb dynamics on the tight 3-sphere

2007/07/07 by F. Bourgeois, Bourgeois, F., K. Cieliebak +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.0707.1068

20 pages, no figures

arxiv created 2007/07/07 · arxiv updated 2009/12/01

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.

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