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Iteration of quasiregular tangent functions in three dimensions

Authors: A. N. Fletcher and D. A. Nicks
Journal: Conform. Geom. Dyn. 16 (2012), 1-21
MSC (2010): Primary 30C65; Secondary 30D05, 37F10
Posted: February 7, 2012
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Abstract: We define a new quasiregular mapping $T:\mathbb{R}^3\to \mathbb{R}^3 \cup \{\infty \}$ that generalizes the tangent function on the complex plane and shares a number of its geometric properties. We investigate the dynamics of the family $\{\lambda T:\lambda >0\}$ , establishing results analogous to those of Devaney and Keen for the meromorphic family $\{z\mapsto \lambda \tan z:\lambda >0\}$ , although the methods used are necessarily original.

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