{"paper":{"title":"Diophantine approximation with nonsingular integral transformations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Arnaldo Nogueira, S.G. Dani","submitted_at":"2019-02-25T12:11:56Z","abstract_excerpt":"Let $\\Gamma$ be the multiplicative semigroup of all $n\\times n$ matrices with integral entries and positive determinant. Let $1\\leq p \\leq n-1$ and $V=\\R^n\\oplus \\cdots \\oplus \\R^n$ ($p$ copies). We consider the componentwise action of $\\Gamma$ on $V$. Let $\\bx\\in V$ be such that $\\Gamma \\bx$ is dense in $V$. We discuss the effectiveness of the approximation of any target point $\\by \\in V$ by the orbit $\\{ \\gamma \\bx \\mid \\gamma \\in \\Gamma\\}$, in terms of $\\norm \\gamma \\norm$, and prove in particular that for all $\\bx$ in the complement of a specific null set described in terms of a certain Di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09219","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"}