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To this end, we generalize a famous result of McMullen, proving that homeomorphic copies of $(\\partial \\Mand)^{k}$ are dense in the support of the $k^{th}$-bifurcation current $T^k_\\bif$ in general families of rational maps, where $\\Mand$ is the Mandelbrot set. As a consequence, we also"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.0862","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-03T07:55:51Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"f82c35c7936e34f3091102b759662d1fc4bb43b614b78e03100d738206ffc3f5","abstract_canon_sha256":"f3992ce2c7be315ea2bcb257597fc5d960d148de15ad00e3459dd0b0eee5d37a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:55.983160Z","signature_b64":"pGxwZVV2UJ6WVFJ7nFFYrNKAFZDG0rsP4bZXTtN730atp9k7oWMof1YfDRnBf/K6VuMwSYulVR+k6cYgYdX8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9d97c6a91d537fbf8edd1688da0d4bf01ed69696def68bfb392b3dfb166ba56","last_reissued_at":"2026-05-18T03:13:55.982288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:55.982288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher bifurcation currents, neutral cycles and the Mandelbrot set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Thomas Gauthier (LAMFA)","submitted_at":"2013-04-03T07:55:51Z","abstract_excerpt":"We prove that given any $\\theta_1,\\ldots,\\theta_{2d-2}\\in \\R\\setminus\\Z$, the support of the bifurcation measure of the moduli space of degree $d$ rational maps coincides with the closure of classes of maps having $2d-2$ neutral cycles of respective multipliers $e^{2i\\pi\\theta_1},\\ldots,e^{2i\\pi\\theta_{2d-2}}$. To this end, we generalize a famous result of McMullen, proving that homeomorphic copies of $(\\partial \\Mand)^{k}$ are dense in the support of the $k^{th}$-bifurcation current $T^k_\\bif$ in general families of rational maps, where $\\Mand$ is the Mandelbrot set. 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