Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space

Abstract

Let $\Gamma$ be a lattice of a semisimple Lie group $L$. Suppose that one parameter 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 $\{g_t\}$ we show that given $x\in L/\Gamma$ for almost every $u\in U$ the trajectory $\{g_{t}ux:0\le t\le T\}$ is uniformly distributed with respect to $\mu$ as $T\to \infty$.

The detailed proof is modified a lot to make the paper easy to read

References in corpus (1)

• Equidistribution from Fractals

Cited by in corpus (1)

• An upper bound of the Hausdorff dimension of singular vectors on affine subspaces