V.I. Arnold, in his paper The algebraic Hopf invariant and its applications published in 1986, considered a compact domain (ômega maiúsculo) in R3 with a smooth boundary and trivial homology and two divergence free vector fields X and Y in (ômega maiúsculo) tangent to the boundary. He defined an asymptotic linking invariant lk(X; Y ) and a Hopf invariant associated to X and Y by the integral I(X; Y ) equal (integral em ômega maiúsculo de alfa produto d-beta) where (d-alfa) equal iX-vol e (d-beta) equal iy- vol. He showed that que I(X; Y ) equal lk(X; Y ). In the present work we extend these definitions of the asymptotic linking invariant lk(fi capital letter,xi capital letter) and the Hopf invariant I(fi maiúsculo,xi capital letter) where (fi capital letter) and (xi capital letter) are actions Rk and Rs, k plus s equal n-1 by volume preserving diffeomorphisms, on the closed unit ball (ômega capital letter n) in and we show lk (fi capital letter, xi capital lette r equal I(ficapital letter ,xi capital letter).