Asymptotic linking of volume-preserving actions of [formula omitted

Abstract

We extend V. Arnold's work on asymptotic linking for two volume preserving flows on a domain in R3 and S3 to volume preserving actions of Rk and Rℓ on certain domains in Rn and also to linking of a volume preserving action of Rk with a closed oriented singular ℓ-dimensional submanifold in Rn, where n=k+ℓ+1.