Complex Representatives, Similarity Invariants, and Iterates in $\mathbf{U}(1,1;\mathbb{H})$

Bingzhe Hou, Cailing Yao, Jiaxing He

We study the similarity classes of matrices in $U(1,1;\mathbb{H})$ and the iterates of their associated quaternionic Möbius transformations. Building on the known elliptic case, we…