  In many regular cases, there exists a (properly defined) limit of iterations
of a function in several real variables, and this limit satisfies the
functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a
vector. This is a special case of a well-known translation equation. In this
paper we present a complete solution to this functional equation in case f is a
continuous function on a single point compactification of a 2-dimensional real
vector space. It appears that, up to conjugation by a homogeneous continuous
function, there are exactly four solutions. Further, in a 1-dimensional case we
present a solution with no regularity assumptions on f.
