Conditions for Infinitely Generated Kleinian Groups with Small Limit Sets
We provide conditions for an infinitely generated Kleinian group to have its exponent of convergence arbitrarily small and the Hausdorff dimension of the limit set less than two. We use theory developed by Patterson to show that the exponent of convergence is small. To obtain the conclusion about the Hausdorff dimension of the limit set of the group we use porosity.
Lazowski, A. (2013). Conditions for infinitely generated Kleinian groups with small limit sets. Journal of Dynamical Systems and Geometric Theories, 11(1-2), 87-97. Doi: 10.1080/1726037X.2013.853513