{"paper":{"title":"On self-affine measures with equal Hausdorff and Lyapunov dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ariel Rapaport","submitted_at":"2015-11-21T15:52:12Z","abstract_excerpt":"Let $\\mu$ be a self-affine measure on $\\mathbb{R}^{d}$ associated to a self-affine IFS $\\{\\varphi_{\\lambda}(x) = A_{\\lambda}x + v_{\\lambda}\\}_{\\lambda\\in\\Lambda}$ and a probability vector $p=(p_{\\lambda})_{\\lambda}>0$. Assume the strong separation condition holds. Let $\\gamma_{1}\\ge...\\ge\\gamma_{d}$ and $D$ be the Lyapunov exponents and dimension corresponding to $\\{A_{\\lambda}\\}_{\\lambda\\in\\Lambda}$ and $p^{\\mathbb{N}}$, and let $\\mathbf{G}$ be the group generated by $\\{A_{\\lambda}\\}_{\\lambda\\in\\Lambda}$. We show that if $\\gamma_{m+1}>\\gamma_{m}=...=\\gamma_{d}$, if $\\mathbf{G}$ acts irreducib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06893","kind":"arxiv","version":1},"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"}