## Iteration of quasiregular tangent functions in three dimensions

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- by A. N. Fletcher and D. A. Nicks PDF
- Conform. Geom. Dyn.
**16**(2012), 1-21 Request permission

## 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.## References

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## Additional Information

**A. N. Fletcher**- Affiliation: University of Warwick, Mathematics Institute, Coventry, England CV4 7AL
- MR Author ID: 749646
**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
- MR Author ID: 862157
- Received by editor(s): December 15, 2011
- Published electronically: February 7, 2012
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**16**(2012), 1-21 - MSC (2010): Primary 30C65; Secondary 30D05, 37F10
- DOI: https://doi.org/10.1090/S1088-4173-2012-00236-6
- MathSciNet review: 2888171