{"paper":{"title":"Biaccessiblility in quadratic Julia sets II: The Siegel and Cremer cases","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Saeed Zakeri","submitted_at":"1998-01-15T00:00:00Z","abstract_excerpt":"Let $f$ be a quadratic polynomial which has an irrationally indifferent fixed point $\\alpha$. Let $z$ be a biaccessible point in the Julia set of $f$. Then:\n  1. In the Siegel case, the orbit of $z$ must eventually hit the critical point of $f$.\n  2. In the Cremer case, the orbit of $z$ must eventually hit the fixed point $\\alpha$. Siegel polynomials with biaccessible critical point certainly exist, but in the Cremer case it is possible that biaccessible points can never exist.\n  As a corollary, we conclude that the set of biaccessible points in the Julia set of a Siegel or Cremer quadratic po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801150","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"}