## Abstract

Let Gamma be a lattice in G = SL(n, R) and X = G/S be a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish the uniform distribution of orbits of Gamma in X analogous to the classical equidistribution on a torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of a Borel subgroup of G.

Translated title of the contribution | Lattice action on the boundary of SL(n,R) |
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Original language | English |

Pages (from-to) | 1817-1837 |

Number of pages | 21 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 23 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2003 |