{"paper":{"title":"A variational principle relating self-affine measures to self-affine sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cagri Sert, Ian D. Morris","submitted_at":"2023-03-06T19:01:27Z","abstract_excerpt":"A breakthrough result of B\\'ar\\'any, Hochman and Rapaport published in 2019 established that every self-affine measure on $\\mathbb{R}^2$ satisfying certain mild non-degeneracy conditions has Hausdorff dimension equal to its Lyapunov dimension. In combination with a variational principle established earlier by Morris and Shmerkin this result implied as a corollary that the attractor of a planar affine iterated function system satisfying the same conditions necessarily has Hausdorff dimension equal to a value proposed by Falconer in 1988. In this article we extend the variational principle of Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03437","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/2303.03437/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"}