Geodesic
Schottky-type groups and minimal sets of horocycle and geodesic flows
Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 35-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the first part of the paper the following conjecture stated by Dal'bo and Starkov is proved: the geodesic flow on a surface $M=\mathbb H^2/\Gamma$ of constant negative curvature has a non-compact non-trivial minimal set if and only if the Fuchsian group $\Gamma$ is infinitely generated or contains a parabolic element. In the second part interesting examples of horocycle flows are constructed: 1) a flow whose restriction to the non-wandering set has no minimal subsets, and 2) a flow without minimal sets. In addition, an example of an infinitely generated discrete subgroup of $\operatorname{SL}(2,\mathbb R)$ with all orbits discrete and dense in $\mathbb R^2$ is constructed. 
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M. S. Kulikov. Schottky-type groups and minimal sets of horocycle and geodesic flows. Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 35-64. http://geodesic.mathdoc.fr/item/SM_2004_195_1_a2/

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