We consider the general non-vanishing, divergence-free vector fields defined on a domain in 3-space and tangent to its boundary. Based on the theory of finite-type invariants, we define a family of invariants for such fields, in the style of Arnold’s asymptotic linking number. Our approach is based on the configuration space integrals due to Bott and Taubes.
R. KOMENDARCZYK and I. VOLIĆ. On volume-preserving vector fields and finite-type invariants of knots. Ergodic Theory and Dynamical Systems, available on CJO2014. doi:10.1017/etds.2014.83.