The straightening theorem for tangent-like maps

Piotr Galązka and Janina Kotus

Vol. 237 (2008), No. 1, 77–85

DOI: 10.2140/pjm.2008.237.77

Abstract

By analogy to polynomial-like maps, we introduce a notion of tangent-like maps. The main result of this paper is the straightening theorem. It says that a tangent-like map is quasiconformally equivalent to some tangent-type function f : ℂ →ℂ ∖{a,b} for a≠b, which is unique up to an affine map. We also prove that quasiconformal conjugacy is conformal on the interior of the filled Julia set.

Keywords

meromorphic functions, Julia set, filled Julia set, polynomial-like maps, hybrid equivalent

Mathematical Subject Classification 2000

Primary: 30D05

Secondary: 37F30

Milestones

Received: 25 July 2007

Accepted: 14 May 2008

Published: 1 September 2008