关于Böttcher坐标与拟正则映射
On Böttcher coordinates and quasiregular maps
摘要：
众所周知，多项式f（z）=a_d z^d（1+o（1））可以由全纯映射φ在无穷邻域内共轭到w \mapsto w^d.这个映射φ在f接近无穷大时称为伯彻坐标。本文对仿射映射与多项式的复合构造了一个Böttcher型坐标，这类映射首先由A.Fletcher和D.Goodman在“Quasirregular mappings of polynomial type in R^2”中研究.作为应用，我们证明了如果h是仿射的，c是复数，则h（z）^2+c不是一致拟正则的.
英文摘要：
It is well-known that a polynomial f(z)=a_d z^d(1+o(1)) can be conjugated by a holomorphic map phi to w \mapsto w^d in a neighbourhood of infinity. This map phi is called a Böttcher coordinate for f near infinity. In this paper we construct a Böttcher type coordinate for compositions of affine mappings and polynomials, a class of mappings first studied in "Quasiregular mappings of polynomial type in R^2" by A.Fletcher and D.Goodman. As an application, we prove that if h is affine and c is a complex number, then h(z)^2+c is not uniformly quasiregular.
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