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.
@article{WBLN_2015__2__A2_0, author = {Pierre Dehornoy}, title = {Asymptotic invariants of 3-dimensional vector fields}, journal = {Winter Braids Lecture Notes}, note = {talk:2}, pages = {1--19}, publisher = {Winter Braids School}, volume = {2}, year = {2015}, doi = {10.5802/wbln.8}, mrnumber = {3705874}, zbl = {1428.37002}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/wbln.8/} }
TY - JOUR AU - Pierre Dehornoy TI - Asymptotic invariants of 3-dimensional vector fields JO - Winter Braids Lecture Notes N1 - talk:2 PY - 2015 SP - 1 EP - 19 VL - 2 PB - Winter Braids School UR - https://proceedings.centre-mersenne.org/articles/10.5802/wbln.8/ DO - 10.5802/wbln.8 LA - en ID - WBLN_2015__2__A2_0 ER -
Pierre Dehornoy. Asymptotic invariants of 3-dimensional vector fields. Winter Braids Lecture Notes, Winter Braids V (Pau, 2015), Volume 2 (2015), Talk no. 2, 19 p. doi : 10.5802/wbln.8. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.8/
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