{"paper":{"title":"Quasisymmetric conjugacy between quadratic dynamics and iterated function systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Boris Solomyak, Kemal Ilgar Ero\\u{g}lu, Steffen Rohde","submitted_at":"2008-06-24T18:43:05Z","abstract_excerpt":"We consider linear iterated function systems (IFS) with a constant contraction ratio in the plane for which the \"overlap set\" $\\Ok$ is finite, and which are \"invertible\" on the attractor $A$, the sense that there is a continuous surjection $q: A\\to A$ whose inverse branches are the contractions of the IFS. The overlap set is the critical set in the sense that $q$ is not a local homeomorphism precisely at $\\Ok$. We suppose also that there is a rational function $p$ with the Julia set $J$ such that $(A,q)$ and $(J,p)$ are conjugate. We prove that if $A$ has bounded turning and $p$ has no parabol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3952","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"}