{"paper":{"title":"Joint spectral radius, Sturmian measures, and the finiteness conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Pollicott, Oliver Jenkinson","submitted_at":"2015-01-14T17:32:00Z","abstract_excerpt":"The joint spectral radius of a pair of 2x2 real matrices $(A_0,A_1)\\in M_2(\\mathbb{R})^2$ is defined to be $r(A_0,A_1)= \\limsup_{n\\to\\infty} \\max \\{\\|A_{i_1}...A_{i_n}\\|^{1/n}: i_j\\in\\{0,1\\}\\}$, the optimal growth rate of the norm of products of these matrices. The Lagarias-Wang finiteness conjecture, asserting that $r(A_0,A_1)$ is always the nth root of the spectral radius of some length-n product $A_{i_1}...A_{i_n}$, has been refuted by Bousch & Mairesse, with subsequent counterexamples presented by Blondel, Theys & Vladimirov; Kozyakin; Hare, Morris, Sidorov & Theys. In this article we intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03419","kind":"arxiv","version":4},"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"}