{"paper":{"title":"The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mitsuhiro Shishikura","submitted_at":"1991-04-12T00:00:00Z","abstract_excerpt":"It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff dimension two and that for a generic $c \\in \\bM$, the Julia set of $z \\mapsto z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the bifurcation of parabolic periodic points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201282","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"}