Geodesic
On free subgroups of $SL(2,\mathbb C)$ with two parabolic generators
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VIII, Tome 155 (1986), pp. 150-155 
M. Yu. Lyubich; V. V. Suvorov. On free subgroups of $SL(2,\mathbb C)$ with two parabolic generators. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VIII, Tome 155 (1986), pp. 150-155. http://geodesic.mathdoc.fr/item/ZNSL_1986_155_a8/
@article{ZNSL_1986_155_a8,
     author = {M. Yu. Lyubich and V. V. Suvorov},
     title = {On free subgroups of $SL(2,\mathbb C)$ with two parabolic generators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--155},
     year = {1986},
     volume = {155},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_155_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $G_\lambda$ be a group generated by a pair of parabolic matrices $A=\left(\begin{smallmatrix}1 & 0 \\ 1 & 1 \end{smallmatrix}\right)$ and $B_\lambda=\left(\begin{smallmatrix}1 & \lambda \\ 0 & 1 \end{smallmatrix}\right)$, $\Gamma_0$ be a set of $\lambda\in\mathbb C$ for which $G_\lambda$ is non-free, $\Gamma=\bar\Gamma_0$. Using the theory of Kleinian groups we prove that both sets $\Gamma$ and $\mathbb C\setminus\Gamma$ are connected. Besides we observe that $\mathbb C\setminus\Gamma_0$ is invariant under a large semigroup of polynomial mappings. Using this observation we show that $\Gamma$ coinsides with the closure of non-discrete groups and with the closure of torsion groups. Finally we describe $\Gamma$ in terms of the dynamics of those polynomial mappings.