Poincare linearizers in higher dimensions

2013/08/23 by Alastair Fletcher, Fletcher, Alastair
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.1308.5180

14 pages, 1 figure

arxiv created 2013/08/23 · arxiv updated 2013/08/26

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↦ 2x. In particular, we show that the fast escaping set of such a linearizer has a spider's web structure.

Related

• On quasiregular linearizers
• A Unified Approach to Quasiregular Linearization in the Plane
• Slow escaping points of quasiregular mappings
• Dynamics of mappings with constant dilatation
• Eventual hyperbolic dimension of entire functions and Poincaré functions of polynomials