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- Title
On the classification of quaternionic Möbius transformations.
- Authors
WENSHENG CAO; PARKER, JOHN R.; XIANTAO WANG
- Abstract
In this paper we consider quaternionic Möbius transformations preserving the unit ball in the quaternions H. In other words, maps of the form g(z) = (az+b)(cz + d)-1 where a, b, c and d all lie in H with the property that |g(z)| < 1 for all |z| < 1. We give an explicit expression for the fixed points of g in terms of a, b, c and d and we use this to classify quaternionic Möbius transformations into six categories determined by their dynamics.
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2004, Vol 137, Issue 2, p349
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004104007868