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We prove an analogous result for unicritical Blaschke products: in the parameter space of degree $d$ unicritical Blaschke products, the parabolic functions are parameterized by an epicycloid with $d-1$ cusps and inside this epicycloid are the parameters which give rise to elliptic functions hav"},"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":"1504.06539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-24T15:23:18Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"c816f55a2827a707e431a10f397ce7a3a5533c372a25654fa70d280fb6a02193","abstract_canon_sha256":"235e434852df55d68bbad61870fd29e66a28e8b5375a0db7cf44d7cdbf4d0041"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:53.348959Z","signature_b64":"SbX7RKHtvORqKYdVAo/57+rwU7+q/O4UZrjljzoxPlypR2PhMN9i0ccTZKcI5Z0XB+gB+YAWhku/OuX55D8TCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c76c7807bbb2a87301a6743548566830000e99bd69f8751f837feb08c0686b2f","last_reissued_at":"2026-05-18T02:17:53.348261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:53.348261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Epicycloids and Blaschke products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Alastair Fletcher, Chunlei Cao, Zhuan Ye","submitted_at":"2015-04-24T15:23:18Z","abstract_excerpt":"It is well known that the bounding curve of the central hyperbolic component of the Multibrot set in the parameter space of unicritical degree $d$ polynomials is an epicycloid with $d-1$ cusps. 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