{"paper":{"title":"Divergent trajectories under diagonal geodesic flow and splitting of discrete subgroups of $\\mathrm{SO}(n,1) \\times \\mathrm{SO}(n,1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lei Yang","submitted_at":"2016-09-14T03:13:23Z","abstract_excerpt":"Let $H = \\mathrm{SO}(n,1)$ and $A = \\{a(t): t \\in \\mathbb{R}\\}$ be a maximal $\\mathbb{R}$-split Cartan subgroup of $H$. Let $\\Gamma \\subset H \\times H$ be a nonuniform lattice in $H \\times H$ and $X_{\\Gamma} : = H \\times H/ \\Gamma$. Let $A_2 : = \\{ a_2(t):=a(t) \\times a(t) : t \\in \\mathbb{R}\\} \\subset A\\times A$ on $X_{\\Gamma}$ and $\\mathcal{D}_{\\Gamma}\\subset X_{\\Gamma}$ denote the collection of points $x \\in X_{\\Gamma}$ such that $a_2(t)x$ diverges as $t \\rightarrow +\\infty$. In this note, we will show that if the Hausdorff dimension of $\\mathcal{D}_{\\Gamma}$ is greater than $\\dim (H\\times H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04118","kind":"arxiv","version":2},"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"}