Asymptotic invariants of 3-dimensional vector fields

Dehornoy, Pierre

Winter Braids V (Pau, 2015), Winter Braids Lecture Notes (2015), Exposé no. 2, 19 p.

In this survey article, we present several constructions of invariants for 3-dimensional volume-preserving vector fields under volume-preserving diffeomorphisms. After introducing helicity, we focus on invariants constructed using knot theory, following Arnol’d’s strategy. Most invariants constructed in this way are actually very close to helicity, but we also present a few that are rather different. We conclude with some open questions.

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