{"paper":{"title":"Pointwise H\\\"older Exponents of the Complex Analogues of the Takagi Function in Random Complex Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.PR"],"primary_cat":"math.DS","authors_text":"Hiroki Sumi, Johannes Jaerisch","submitted_at":"2016-03-29T12:34:59Z","abstract_excerpt":"We investigate the H\\\"older regularity of the function $T$ of the probability of tending to one minimal set, the partial derivatives of $T$ with respect to the probability parameters, which can be regarded as complex analogues of the Takagi function, and the higher partial derivatives $C$ of $T.$ Our main result gives a dynamical description of the pointwise H\\\"older exponents of $T$ and $C$, which allows us to determine the spectrum of pointwise H\\\"older exponents by employing the multifractal formalism in ergodic theory. Also, we prove that the bottom of the spectrum $\\alpha_{-}$ is strictly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08744","kind":"arxiv","version":5},"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"}