Solly Coles

Helicity and linking for 3-dimensional Anosov flows

On a closed 3-manifold, the helicity of a volume-preserving flow is an invariant originally used for solving variational problems in magnetohydrodynamics. Helicity was introduced by Moffatt, who indicated that helicity measures the total amount of linking of flow trajectories. When the manifold is a real homology 3-sphere, Arnol'd and Vogel proved that helicity can be evaluated in terms of the linking numbers of knots constructed by closing up flow trajectories with geodesic arcs. In this talk we will discuss a similar characterisation of helicity for Anosov flows, in terms of weighted averages of linking numbers of periodic orbits. (This is joint work with Richard Sharp.)