Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space
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Abstract:
Let $\Gamma$ be a lattice of a semisimple Lie group $L$. Suppose that a one parameter $\operatorname {Ad}$-diagonalizable subgroup $\{g_t\}$ of $L$ acts ergodically on $L/\Gamma$ with respect to the probability Haar measure $\mu$. For certain proper subgroup $U$ of the unstable horospherical subgroup of $\{g_t\}$ and certain $x\in L/\Gamma$ we show that for almost every $u\in U$ the trajectory $\{g_tux: 0\le t\le T\}$ is equidistributed with respect to $\mu$ as $T\to \infty$.References
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Additional Information
- Ronggang Shi
- Affiliation: Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
- MR Author ID: 963201
- Email: ronggang@fudan.edu.cn
- Received by editor(s): December 1, 2017
- Received by editor(s) in revised form: May 14, 2019, and October 2, 2019
- Published electronically: March 10, 2020
- Additional Notes: The author was supported by ERC starter grant DLGAPS 279893 and NSFC 11871158
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 4189-4221
- MSC (2010): Primary 28A33; Secondary 37C85, 37A30
- DOI: https://doi.org/10.1090/tran/8028
- MathSciNet review: 4105521