2014/08/11 by Alastair Fletcher, Fletcher, Alastair, Douglas Macclure +1
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS
paper · pdf · doi:10.48550/arxiv.1408.2414
arxiv created 2014/08/11 · arxiv updated 2014/08/12
Linearization is a well-known concept in complex dynamics. If p is a polynomial and z0 is a repelling fixed point, then there is an entire function L which conjugates p to the linear map z↦ p'(z0)z. This notion of linearization carries over into the quasiregular setting, in the context of repelling fixed points of uniformly quasiregular mappings. In this article, we investigate how linearizers arising from the same uqr mapping and the same repelling fixed point are related. In particular, any linearizer arising from a uqr solution to a Schröder equation is shown to be automorphic with respect to some quasiconformal group.