{"paper":{"title":"On the quasisymmetrical classification of infinitely renormalizable maps: I. Maps with Feigenbaum's topology.","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yunping Jiang","submitted_at":"1991-10-11T00:00:00Z","abstract_excerpt":"A semigroup (dynamical system) generated by $C^{1+\\alpha}$-contracting mappings is considered. We call a such semigroup regular if the maximum $K$ of the conformal dilatations of generators, the maximum $l$ of the norms of the derivatives of generators and the smoothness $\\alpha$ of the generators satisfy a compatibility condition $K< 1/l^{\\alpha}$. We prove the {\\em geometric distortion lemma} for a regular semigroup generated by $C^{1+\\alpha}$-contracting mappings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201294","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"}