On Böttcher Coordinates and Quasiregular Maps
نویسندگان
چکیده
It is well-known that a polynomial f(z) = adz(1 + o(1)) can be conjugated by a holomorphic map φ to w 7→ w in a neighbourhood of in nity. This map φ is called a Böttcher coordinate for f near in nity. In this paper we construct a Böttcher type coordinate for compositions of a ne mappings and polynomials, a class of mappings rst studied in [9]. As an application, we prove that if h is a ne and c ∈ C, then h(z) + c is not uniformly quasiregular. MSC 2010: 30C65 (Primary), 30D05, 37F10, 37F45 (Secondary).
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