  We give a complete description of the closure of the space of one-generator
closed subgroups of PSL2(R) for the Chabauty topology, by computing explicitly
the matrices associated with elements of Aut(D) = PSL2(R), and finding
quantities parametrizing the limit cases. Along the way, we investigate under
what conditions sequences of maps transform convergent sequences of closed
subsets of the domain into convergent sequences of closed subsets of the range.
In particular, this allows us to compute certain geometric limits of PSL2(R)
only by looking at the Hausdorff limit of some closed subsets of C.
