{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:W3UQVDHMLPI4NTFHTA4G4X5LOE","short_pith_number":"pith:W3UQVDHM","schema_version":"1.0","canonical_sha256":"b6e90a8cec5bd1c6cca798386e5fab7126d952f180bc295f7496e05182021c6b","source":{"kind":"arxiv","id":"1304.4864","version":1},"attestation_state":"computed","paper":{"title":"On the Fibonacci complex dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ali Messaoudi, el Houcein el Abdalaoui, Olivier Sester, Sylvain Bonnot","submitted_at":"2013-04-17T15:42:37Z","abstract_excerpt":"We consider in this paper a sequence of complex analytic functions constructed by the following procedure $f_n(z)=f_{n-1}(z)f_{n-2}(z)+c$, where $c\\in\\C$ is a parameter. Our aim is to give a thorough dynamical study of this family, in particular we are able to extend the familiar notions of Julia sets and Green function and to analyze their properties. As a consequence, we extend some well-known results. Finally we study in detail the case where $c$ is small."},"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":"1304.4864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-04-17T15:42:37Z","cross_cats_sorted":[],"title_canon_sha256":"3e28392739787927d047b475f19926530fbb6aa5271166d144c2c9b85b4ac2b0","abstract_canon_sha256":"9452831326800277ce81d5395289284f49d6b5004fb574d5938fb84dfae8caa8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:43.449924Z","signature_b64":"Q8XhEN0u+WIshcy2DWrddLW/FN5ighyA9+SnjEjgzdekGSSInpCNPBLsEV/1EjBztROYDrUBlEKQpFQyDnLEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6e90a8cec5bd1c6cca798386e5fab7126d952f180bc295f7496e05182021c6b","last_reissued_at":"2026-05-18T03:27:43.449279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:43.449279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Fibonacci complex dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ali Messaoudi, el Houcein el Abdalaoui, Olivier Sester, Sylvain Bonnot","submitted_at":"2013-04-17T15:42:37Z","abstract_excerpt":"We consider in this paper a sequence of complex analytic functions constructed by the following procedure $f_n(z)=f_{n-1}(z)f_{n-2}(z)+c$, where $c\\in\\C$ is a parameter. Our aim is to give a thorough dynamical study of this family, in particular we are able to extend the familiar notions of Julia sets and Green function and to analyze their properties. As a consequence, we extend some well-known results. Finally we study in detail the case where $c$ is small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4864","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.4864","created_at":"2026-05-18T03:27:43.449377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4864v1","created_at":"2026-05-18T03:27:43.449377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4864","created_at":"2026-05-18T03:27:43.449377+00:00"},{"alias_kind":"pith_short_12","alias_value":"W3UQVDHMLPI4","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"W3UQVDHMLPI4NTFH","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"W3UQVDHM","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE","json":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE.json","graph_json":"https://pith.science/api/pith-number/W3UQVDHMLPI4NTFHTA4G4X5LOE/graph.json","events_json":"https://pith.science/api/pith-number/W3UQVDHMLPI4NTFHTA4G4X5LOE/events.json","paper":"https://pith.science/paper/W3UQVDHM"},"agent_actions":{"view_html":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE","download_json":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE.json","view_paper":"https://pith.science/paper/W3UQVDHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4864&json=true","fetch_graph":"https://pith.science/api/pith-number/W3UQVDHMLPI4NTFHTA4G4X5LOE/graph.json","fetch_events":"https://pith.science/api/pith-number/W3UQVDHMLPI4NTFHTA4G4X5LOE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE/action/storage_attestation","attest_author":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE/action/author_attestation","sign_citation":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE/action/citation_signature","submit_replication":"https://pith.science/pith/W3UQVDHMLPI4NTFHTA4G4X5LOE/action/replication_record"}},"created_at":"2026-05-18T03:27:43.449377+00:00","updated_at":"2026-05-18T03:27:43.449377+00:00"}