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Iteration of quasiregular tangent functions in three dimensions
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Fletcher, Alastair and Nicks, Daniel A.. (2012) Iteration of quasiregular tangent functions in three dimensions. Conformal Geometry and Dynamics, Vol.16 . pp. 1-21. ISSN 1088-4173
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Official URL: http://dx.doi.org/10.1090/S1088-4173-2012-00236-6
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Conformal Geometry and Dynamics |
| Publisher: | American Mathematical Society |
| ISSN: | 1088-4173 |
| Date: | 2012 |
| Volume: | Vol.16 |
| Number of Pages: | 22 |
| Page Range: | pp. 1-21 |
| Identification Number: | 10.1090/S1088-4173-2012-00236-6 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48346 |
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