Periodic orbits of Euler vector fields on 3-manifolds

2010/11/23 by Ana Rechtman, Rechtman, Ana
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1011.5253

Abstract

In this paper we study the existence of 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 C² the flow always posses a periodic orbit unless the manifold is a torus bundle over the circle. This result generalizes preavious result of J. Etnyre and R. Ghrist by weakening the real analytic hypothesis to C².

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