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In this paper we study a \\textit{non-autonomous} parabolic bifurcation. We focus on the case of $f_0(z)=\\frac{z}{1-z}$. Given a sequence $\\{\\epsilon_i\\}_{1\\leq i\\leq N}$, we denote $f_n(z) = f_0(z) + \\epsilon_n^2$. We give sufficient and necessary conditions on the sequence $\\{\\epsilon_i\\}$ that imply that $f_{N}\\ci"},"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":"1905.00937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-05-02T19:17:07Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a7a46ef5f3fd161f1f4a852fd72d8934bb3b617176037ce1e7816699e5f7b862","abstract_canon_sha256":"ff5e24399815da066a4ed953813babf17249264a75a1c2a8b2af93c5411f7411"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:08.200729Z","signature_b64":"5iNnA2AWa++GaKFXoDwp/ECs4qdSKvt6H6vGFa0fPUKkFfAc96yMKV2EX8Vm0RK/70BntIss2tlcx22x9TEHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00dd7517a10fb4d10b8bd08c3612951048ec2d9b35f7616755788d27c72054b8","last_reissued_at":"2026-05-17T23:47:08.200010Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:08.200010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-autonomous Parabolic Bifurcation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Liz Vivas","submitted_at":"2019-05-02T19:17:07Z","abstract_excerpt":"Let $f(z) = z+z^2+O(z^3)$ and $f_\\epsilon(z) = f(z) + \\epsilon^2$. 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