{"paper":{"title":"Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ronggang Shi","submitted_at":"2014-05-08T19:54:31Z","abstract_excerpt":"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 $\\{g_tux: 0\\le t\\le T\\}$ is uniformly distributed with respect to $\\mu$ as $T\\to \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2067","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}