{"paper":{"title":"Multifractal Formalism for generalised local dimension spectra of Gibbs measures on the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hiroki Sumi, Johannes Jaerisch","submitted_at":"2019-02-19T09:26:13Z","abstract_excerpt":"We refine the multifractal formalism for the local dimension of a Gibbs measure $\\mu$ supported on the attractor $\\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\\alpha\\in \\mathbb{R}$, we establish the formalism for the Hausdorff dimension of level sets of points $x\\in\\Lambda$ for which the $\\mu$-measure of a ball of radius $r_{n}$ centered at $x$ obeys a power law $r_{n}{}^{\\alpha}$, for a sequence $r_{n}\\rightarrow0$. This allows us to investigate the H\\\"older regularity of various fractal functions, such as distribution functions and conjugacy maps ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06962","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"}