Conical limit points and the Cannon-Thurston map

@article{Jeon2014ConicalLP,
  title={Conical limit points and the Cannon-Thurston map},
  author={Woojin Jeon and Ilya Kapovich and Christopher J. Leininger and Ken'ichi Ohshika},
  journal={arXiv: Group Theory},
  year={2014}
}
Let $G$ be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space $Z$ so that there exists a continuous $G$-equivariant map $i:\partial G\to Z$, which we call a \emph{Cannon-Thurston map}. We obtain two characterzations (a dynamical one and a geometric one) of conical limit points in $Z$ in terms of their pre-images under the Cannon-Thurston map $i$. As an application we prove, under the extra assumption that the action of $G$ on $Z$ has no accidental… 
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