  For a polynomial p with a repelling fixed point w, we consider Poincar\'{e}
functions of p at w, i.e. entire functions L which satisfy L(0)=w and
p(L(z))=L(p'(w)*z) for all z in the complex plane. We show that if the
component of the Julia set of p that contains w equals {w}, then the (fast)
escaping set of L is a spider's web; in particular it is connected. More
precisely, we classify all linearizers of polynomials with regards to the
spider's web structure of the set of all points which escape faster than the
iterates of the maximum modulus function at a sufficiently large point.
