Asymptotic linking of volume-preserving actions of ${\mathbb R}^k$

Abstract: We extend V. Arnold's theory of asymptotic linking for two volume preserving flows on a domain in

{m a t h b b R}^{3}

and

S^{3}

to volume preserving actions of

{m a t h b b R}^{k}

and

{m a t h b b R}^{e} l l

on certain domains in

{m a t h b b R}^{n}

and also to linking of a volume preserving action of

{m a t h b b R}^{k}

with a closed oriented singular

e l l

-dimensional submanifold in

{m a t h b b R}^{n}

, where

n = k + e l l + 1

. We also extend the Biot-Savart formula to higher dimensions.

This page was built for publication: Asymptotic linking of volume-preserving actions of ${\mathbb R}^k$