Epimorphic subgroups and invariant measures. (English) Zbl 0843.28008
Author’s abstract: “It is shown that a probability measure on a homogeneous space \(\Gamma\backslash G\) which is invariant under a subgroup \(H< G\) which is epimorphic in a subgroup \(L< G\) is invariant under \(L\). When \(L= G\) we obtain a subgroup \(H\) such that for any lattice \(\Gamma< G\) its action on \(\Gamma\backslash G\) is uniquely ergodic”.
Reviewer: M.Denker (Göttingen)
MSC:
| 28D05 | Measure-preserving transformations |
| 37A99 | Ergodic theory |
| 54H20 | Topological dynamics (MSC2010) |
References:
| [1] | Dani, Adv. Sov. Math. 16 pp 91– (1993) |
| [2] | DOI: 10.1007/BF01453567 · Zbl 0679.22007 · doi:10.1007/BF01453567 |
| [3] | Dani, Dynamical Systems and Ergodic theory 23 pp 179– (1989) |
| [4] | DOI: 10.1007/BF01578067 · Zbl 0368.28021 · doi:10.1007/BF01578067 |
| [5] | DOI: 10.1007/BF01446574 · Zbl 0702.22014 · doi:10.1007/BF01446574 |
| [6] | DOI: 10.1215/S0012-7094-84-05110-X · Zbl 0547.20042 · doi:10.1215/S0012-7094-84-05110-X |
| [7] | DOI: 10.2307/2944357 · Zbl 0763.28012 · doi:10.2307/2944357 |
| [8] | DOI: 10.1215/S0012-7094-91-06311-8 · Zbl 0733.22007 · doi:10.1215/S0012-7094-91-06311-8 |
| [9] | Raghunathan, Discrete Subgroup of Lie Groups (1972) · Zbl 0254.22005 · doi:10.1007/978-3-642-86426-1 |
| [10] | Moore, Pac. J. Math. 86 pp 155– (1980) · Zbl 0446.22014 · doi:10.2140/pjm.1980.86.155 |
| [11] | Margulis, Proc. Int. Congress of Mathematicians (Kyoto, 1990) pp 193– (1991) |
| [12] | DOI: 10.1007/BF01895839 · Zbl 0801.22008 · doi:10.1007/BF01895839 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
