Schottky-type groups and minimal sets of horocycle and geodesic flows
Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 35-64
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{SM_2004_195_1_a2,
author = {M. S. Kulikov},
title = {Schottky-type groups and minimal sets of horocycle and geodesic flows},
journal = {Sbornik. Mathematics},
pages = {35--64},
publisher = {mathdoc},
volume = {195},
number = {1},
year = {2004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2004_195_1_a2/}
}
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/