Comptes Rendus
no. 6
Dynamical Systems
The horocycle flow without minimal sets
[Le flot horicyclique sans ensemble minimal]

Présenté par : Étienne Ghys

M. Kulikov1
1 Theory of Dynamical Systems, Mathematics Department, Moscow State University, Moscow, 119992, Russia
Comptes Rendus. Mathématique, Volume 338 (2004) no. 6, pp. 477-480.

On construit un exemple de groupe Fuchsien pour lequel le flot horocyclique est sans ensemble minimal.

We construct an example of a Fuchsian group such that the corresponding horocycle flow has no minimal sets.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.12.027
M. Kulikov 1

1 Theory of Dynamical Systems, Mathematics Department, Moscow State University, Moscow, 119992, Russia 
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M. Kulikov. The horocycle flow without minimal sets. Comptes Rendus. Mathématique, Volume 338 (2004) no. 6, pp. 477-480. doi : 10.1016/j.crma.2003.12.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.027/

[1] A.F. Beardon The Geometry of Discrete Groups, Springer-Verlag, New York, 1983

[2] J.-C. Beniere; G. Meigniez Flows without minimal set, Ergodic Theory Dynamical Systems, Volume 19 (1999) no. 1, pp. 21-30

[3] F. Dal'bo; A.N. Starkov On classification of limit points of infinitely generated Schottky groups, J. Dyn. Contr. Sys., Volume 6 (2000) no. 4, pp. 561-578

[4] E. Ghys, Dynamique des flots unipotents sur les espaces homogenes, Sem. Bourbaki, vol. 1991/92, Asterisque No. 206 (1992), Exp. No. 747, 3, pp. 93–136

[5] T. Inaba An example of a flow on a non-compact surface without minimal set, Ergodic Theory Dynamical Systems, Volume 19 (1999) no. 1, pp. 31-33

[6] M.S. Kulikov Groups of Schottky type and minimal sets of the geodesic flows, Mat. Sb., Volume 195 (2004) no. 1, pp. 37-68 (in Russian)

[7] A.N. Starkov Fuchsian Groups from the dynamical viewpoint, J. Dyn. Con. Sys., Volume 1 (1995) no. 3, pp. 427-445

[8] A.N. Starkov Dynamical Systems on Homogeneous Flows, Transc. Math. Monographs, vol. 190, American Mathematical Society, 2000

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☆ This work is supported by grant No. NSh-457.2003.1 of The Ministry of Industry and Science of Russia.

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