Periodic orbits of Euler vector fields on 3-manifolds

Details Periodic orbits of Euler vector fields on 3-manifolds Periodic orbits of Euler vector fields on 3-manifolds

2010-11-23

arxiv.org/abs/1011.5253v2

Mathematics

Dynamical Systems

Scientific paper

In this paper we study periodic orbits in the flow of non-singular steady Euler fields X on closed 3-manifolds, that is X is a solution of time independent Euler equations. We show that when X is C^2 the flow always posses a periodic orbit, unless the manifold is a torus bundle over the circle. Moreover, we show that if the ambient manifold is the three sphere, there exist an unknotted periodic orbit. These results generalize previous results of J. Etnyre and R. Ghrist by weakening the real analytic hypothesis to C^2.

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