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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… (More)

There exist uniformly quasiregular maps $$f:\mathbb {R}^3 \rightarrow \mathbb {R}^3$$f:R3→R3 whose Julia sets are wild Cantor sets.

In this article, we investigate the boundary of the escaping set I(f) for quasiregular mappings on R, both in the uniformly quasiregular case and in the polynomial type case. The aim is to show that… (More)

It is well-known that the Julia set J(f) of a rational map f : C → C is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus, with the bound depending only on f . In… (More)

It is shown that if f is an analytic function of sufficiently small exponential type in the right half-plane, which takes integer values on a subset of the positive integers having positive lower… (More)

Elliptic Möbius transformations of the unit disk are those for which there is a fixed point in D. It is not hard to classify which Möbius transformations are elliptic in terms of the parameters. The… (More)

The study of quadratic polynomials is a foundational part of modern complex dynamics. In this article, we study quasiregular counterparts to these in the plane. More specifically, let h : C → C be an… (More)