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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.04118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-14T03:13:23Z","cross_cats_sorted":[],"title_canon_sha256":"d9fff19e0c2726a4ca27123706917064a7fcd23a652937b507391ab108adc943","abstract_canon_sha256":"c8dd8545bc50e8b21b6784a67f03c85f0bfedc6c7105940bc1e5746d992c8986"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:16.306621Z","signature_b64":"ZEdr1LLw580B4h9fYwB3OaIWqwbWybhJ28Y+8LtU5d1ftrHNz5xB8oFEaaLqO6NA5Hi6WTfAn6RqupcwOqtbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9572175556f7712305e1a81ba49206e7eedc4a1dd4ed59e211d739c5ecb58d9","last_reissued_at":"2026-05-17T23:47:16.306116Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:16.306116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $t \\rightarrow +\\infty$. 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