{"paper":{"title":"Bounded orbits of diagonalizable flows on $\\rm{SL}_3(\\mathbb{R})/\\rm{SL}_3(\\mathbb{Z})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Kleinbock, Jinpeng An, Lifan Guan","submitted_at":"2015-01-22T07:22:05Z","abstract_excerpt":"We prove that for any countably many one-parameter diagonalizable subgroups $F_n$ of $\\rm{SL}_3(\\mathbb{R})$, the set of $\\Lambda\\in\\rm{SL}_3(\\mathbb{R})/\\rm{SL}_3(\\mathbb{Z})$ such that all the orbits $F_n\\Lambda$ are bounded has full Hausdorff dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05409","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"}