{"paper":{"title":"Dynamics on the space of 2-lattices in 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Oliver Sargent, Uri Shapira","submitted_at":"2017-08-15T11:50:43Z","abstract_excerpt":"We study the dynamics of $SL_3(\\mathbb{R})$ and its subgroups on the homogeneous space $X$ consisting of homothety classes of rank-2 discrete subgroups of $\\mathbb{R}^3$. We focus on the case where the acting group is Zariski dense in either $SL_3(\\mathbb{R})$ or $SO(2,1)(\\mathbb{R})$. Using techniques of Benoist and Quint we prove that for a compactly supported probability measure $\\mu$ on $SL_3(\\mathbb{R})$ whose support generates a group which is Zariski dense in $SL_3(\\mathbb{R})$, there exists a unique $\\mu$-stationary probability measure on $X$. When the Zariski closure is $SO(2,1)(\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04464","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"}