Iteration of quasiregular tangent functions in three dimensions

Fletcher, A.; Nicks, D.

doi:10.1090/S1088-4173-2012-00236-6

Iteration of quasiregular tangent functions in three dimensions
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by A. N. Fletcher and D. A. Nicks

Conform. Geom. Dyn. 16 (2012), 1-21

DOI: https://doi.org/10.1090/S1088-4173-2012-00236-6

Published electronically: 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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