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arXiv · 1308.5180

Poincare linearizers in higher dimensions

Alastair Fletcher
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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 $\R^m$ 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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Alastair Fletcher. 2013-08-23. Poincare linearizers in higher dimensions. https://arxiv.org/abs/1308.5180

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