Kulkarni limit sets for cyclic quaternionic projective groups

We consider the natural action of the quaternionic projective linear group $\mathrm{P}\mathrm{S}\mathrm{L}(n+1,\mathbb{H})$ on the quaternionic projective space ${\mathbb{P}}_{\mathbb{H}}^n$. We compute the Kulkarni limit sets for the cyclic subgroups of $\mathrm{P}\mathrm{S}\mathrm{L}(n+1,\mathbb{H})$.