Comptes Rendus
no. 6
Dynamical Systems
The horocycle flow without minimal sets

Presented by: 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.

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

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

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.12.027

M. Kulikov 1

1 Theory of Dynamical Systems, Mathematics Department, Moscow State University, Moscow, 119992, Russia 
@article{CRMATH_2004__338_6_477_0,
     author = {M. Kulikov},
     title = {The horocycle flow without minimal sets},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {477--480},
     publisher = {Elsevier},
     volume = {338},
     number = {6},
     year = {2004},
     doi = {10.1016/j.crma.2003.12.027},
     language = {en},
}
TY  - JOUR
AU  - M. Kulikov
TI  - The horocycle flow without minimal sets
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 477
EP  - 480
VL  - 338
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2003.12.027
LA  - en
ID  - CRMATH_2004__338_6_477_0
ER  - 
%0 Journal Article
%A M. Kulikov
%T The horocycle flow without minimal sets
%J Comptes Rendus. Mathématique
%D 2004
%P 477-480
%V 338
%N 6
%I Elsevier
%R 10.1016/j.crma.2003.12.027
%G en
%F CRMATH_2004__338_6_477_0
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

Cited by Sources:

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

Comments - Policy