On effective equidistribution for quotients of \(\mathrm{SL}(d, \mathbb{R} )\). (English) Zbl 1481.22008
Summary: We prove the first case of polynomially effective equidistribution of closed orbits of semisimple groups with nontrivial centralizer. The proof relies on uniform pectral gap, builds on, and extends work of the second author et al. [Invent. Math. 177, No. 1, 137–212 (2009; Zbl 1176.37003)].
MSC:
| 22E40 | Discrete subgroups of Lie groups |
| 22E46 | Semisimple Lie groups and their representations |
| 37A17 | Homogeneous flows |
| 37A15 | General groups of measure-preserving transformations and dynamical systems |
| 37C85 | Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) |
Citations:
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