# Questions tagged [hyperbolic-groups]

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### Function on the Cartesian product of group-orbits

Let $\Gamma$ be a group generated by two matrices as follows: $\Gamma:= \bigg\langle \begin{bmatrix}1&0\\3&1\end{bmatrix},\begin{bmatrix}13&12\\12&13\end{bmatrix} \bigg\rangle$ For ...
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### G-invariance of set of points fixed by loxodromic elements in G

Let G be a non-elementary subgroup of Mobius transformations. How can we show that the set of points fixed by loxodromic elements in G is G-invariant? I proved it by directly computations, but I ...
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### About limit set of non-elementary Fuchsian group

I am reading a note on hyperbolic surfaces (http://bicmr.pku.edu.cn/~wyang/132382/notes2.pdf). In page 35, there is a theorem stated that: The limit set of a non-elementary Fuchsian group is the ...
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### Cusp set is dense in boundary of hyperbolic plane

Let $\Gamma$ be a Fuchsian group such that $\mathbb{H}/\Gamma$ is a finite-area hyperbolic surface with some cusps. How can we show that cusp set of $\Gamma$ is dense in the boundary of $\mathbb{H}$? ...
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