Poincaré linearizers in higher dimensions

Fletcher, Alastair

doi:10.1090/S0002-9939-2015-12462-8

Poincaré linearizers in higher dimensions
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Proc. Amer. Math. Soc. 143 (2015), 2543-2557 Request permission

Abstract:

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 Poincaré 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 Poincaré 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.

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