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Conformal Geometry and Dynamics

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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
Published electronically: February 7, 2012
MathSciNet review: 2888171
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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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Additional Information

A. N. Fletcher
Affiliation: University of Warwick, Mathematics Institute, Coventry, England CV4 7AL

D. A. Nicks
Affiliation: Open University, Department of Mathematics and Statistics, Milton Keynes, England MK7 6AA
Address at time of publication: School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

Received by editor(s): December 15, 2011
Published electronically: February 7, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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