Poincare linearizers in higher dimensions

It is well-known that a holomorphic function near a repelling fixed point may be conjugated to a linear function. The function which conjugates is called a Poincar'e linearizer and may be extended to a transcendental entire function in the plane. In this paper, we study the dynamics of a higher dimensional generalization of Poincar'e linearizers. These arise by conjugating a uniformly quasiregular mapping in ${\mathbb{R}}^m$ near a repelling fixed point to the mapping $x\mapsto 2x$. In particular, we show that the fast escaping set of such a linearizer has a spider’s web structure.