Conjugacy classification of quaternionic Möbius transformations

Parker, John R.; Short, Ian

Abstract

It is well known that the dynamics and conjugacy class of a complex Möbius transformation can be determined from a simple rational function of the coefficients of the transformation. We study the group of quaternionic Möbius transformations and identify simple rational functions of the coefficients of the transformations that determine dynamics and conjugacy.

Citation

Parker, J. R., & Short, I. (2009). Conjugacy classification of quaternionic Möbius transformations. Computational Methods and Function Theory - Springer, 9(1), 13-25. https://doi.org/10.1007/bf03321711

• Journal Article Type: Article
• Publication Date: Jan 1, 2009
• Deposit Date: Nov 6, 2009
• Publicly Available Date: Jan 3, 2013
• Journal: Computational Methods and Function Theory - Springer
• Print ISSN: 1617-9447
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 1
• Pages: 13-25
• DOI: https://doi.org/10.1007/bf03321711
• Keywords: Möbius transformations, Quaternions, Conjugacy, Dynamics.
• Publisher URL: http://www.heldermann.de/CMF/CMF09/CMF091/cmf09002.htm