Asymptotic invariants of 3-dimensional vector fields
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.

DOI : 10.5802/wbln.8
Dehornoy, Pierre 1

1 Institut Fourier, Université Grenoble Alpes 100 rue des Maths - BP 74 38402 St Martin d’Hères, France
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Dehornoy, Pierre. Asymptotic invariants of 3-dimensional vector fields, dans Winter Braids V (Pau, 2015), Winter Braids Lecture Notes (2015), Exposé no. 2, 19 p. doi : 10.5802/wbln.8. http://archive.numdam.org/articles/10.5802/wbln.8/

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