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We describe dynamical prope"},"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":"1710.03385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-10T03:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"1bf3400c5e9992afaf87aacf97f9585dc5c00b3395eef2529d7d16299bb729a9","abstract_canon_sha256":"270c2c9679a25d0f9cb9ca1900be1be7b69f36da5bd44e1237299a88bac72902"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:12.110630Z","signature_b64":"t3J6Uy3Yc+mDOk4n3NibGRelLUgd4AYq/f8UxnRIRxgZBwGRluxqfr9Za/kJwCGqdIdsVpK3agwihUR/du/mDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ef5ba974b8adefec355879aaffdc6a19fa99ea792507bcdd9afeaee6ee80447","last_reissued_at":"2026-05-18T00:33:12.110052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:12.110052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correspondences in complex dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Siqueira, Luna Lomonaco, Shaun Bullett","submitted_at":"2017-10-10T03:06:34Z","abstract_excerpt":"This paper surveys some recent results concerning the dynamics of two families of holomorphic correspondences, namely ${\\mathcal F}_a:z \\to w$ defined by the relation $$\\left( \\frac{aw-1}{w-1} \\right)^2 + \\left( \\frac{aw-1}{w-1} \\right) \\left( \\frac{az +1}{z+1} \\right) + \\left( \\frac{az+1}{z+1} \\right)^2 =3,$$ and $$\\mathbf{f}_c(z)=z^{\\beta} +c, \\mbox{ where } 1<\\beta=p/q \\in \\mathbb{Q},$$ which is the correspondence $\\mathbf{f}_c:z \\to w$ defined by the relation $$(w-c)^q=z^p.$$ Both can be regarded as generalizations of the family of quadratic maps $f_c(z)=z^2+c$. 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