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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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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.
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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