{"paper":{"title":"On the dimension of limit sets on $\\mathbb{P}(\\mathbb{R}^3)$ via stationary measures: the theory and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.GT","math.PR"],"primary_cat":"math.DS","authors_text":"Disheng Xu, Jialun Li, Wenyu Pan","submitted_at":"2023-11-17T01:18:15Z","abstract_excerpt":"This paper investigates the (semi)group action of $\\mathrm{SL}_3(\\mathbb{R})$ on $\\mathbb{P}(\\mathbb{R}^3)$, a primary example of non-conformal, non-linear, and non-strictly contracting action. We study the Hausdorff dimension of a dynamically defined limit set in $\\mathbb{P}(\\mathbb{R}^3)$ and generalize the classical Patterson-Sullivan formula using the approach of stationary measures.\n  The two main examples are Anosov representations in $\\mathrm{SL}_3(\\mathbb{R})$ and the Rauzy gasket.\n  1. For Anosov representations in $\\mathrm{SL}_3(\\mathbb{R})$, we establish a sharp lower bound for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.10265","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.10265/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}