{"paper":{"title":"Admissibility of kneading sequences and structure of Hubbard trees for quadratic polynomials","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Dierk Schleicher, Henk Bruin","submitted_at":"2008-01-30T12:36:09Z","abstract_excerpt":"Hubbard trees are invariant trees connecting the points of the critical orbits of postcritically finite polynomials. Douady and Hubbard \\cite{Orsay} introduced these trees and showed that they encode the essential information of Julia sets in a combinatorial way. The itinerary of the critical orbit within the Hubbard tree is encoded by a (pre)periodic sequence on $\\{\\0,\\1\\}$ called \\emph{kneading sequence}.\n  We prove that the kneading sequence completely encodes the Hubbard tree and its dynamics, and we show how to reconstruct the tree and in particular its branch points (together with their "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.4662","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"}