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We give a complete description of the closure of the space of one-generatorclosed subgroups of PSL2(R) for the Chabauty topology, by computing explicitlythe matrices associated with elements of Aut(D) = PSL2(R), and findingquantities parametrizing the limit cases. Along the way, we investigate underwhat conditions sequences of maps transform convergent sequences of closedsubsets 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.

The Space of Geometric Limits of One-generator Closed Subgroups of PSL2(R)