{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:EMHKOO4L3PUTSRL7UXGLFSAVFQ","short_pith_number":"pith:EMHKOO4L","schema_version":"1.0","canonical_sha256":"230ea73b8bdbe939457fa5ccb2c8152c22988ff5445b201fedee6e5f3611caab","source":{"kind":"arxiv","id":"0905.1390","version":4},"attestation_state":"computed","paper":{"title":"Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Denis Gaidashev, Tomas Johnson","submitted_at":"2009-05-09T09:33:41Z","abstract_excerpt":"It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\\fR}^2$. A renormalization approach has been used in \\cite{EKW1} and \\cite{EKW2} in a computer-assisted proof of existence of a \"universal\" area-preserving map $F_*$ -- a map with orbits of all binary periods $2^k, k \\in \\fN$. In this paper, we consider maps in some neighbourhood of $F_*$ and study their dynamics.\n  We first demonstrate that the map $F_*$ admits a \"bi-infinite heteroclinic tangle\": a sequence of periodic points $\\{z_k\\}$, $k \\in \\fZ$, |z_k| \\conve"},"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":"0905.1390","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-09T09:33:41Z","cross_cats_sorted":[],"title_canon_sha256":"0c221457cf8b367a50e5d1c773c4db158684330eec9e3e9508705ed14b85da60","abstract_canon_sha256":"8066be8e565e736a14f56690555cc4fe95c78a6b55f068619a5bb91f26aad198"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:46.184174Z","signature_b64":"i1CgjpFiAMT+3Lx10eqEHk6PhModKa6UruOitXUpxmgTnJNfExs6oiFZs4i5WZED2mV4e3FujLH6SRs/UTQYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"230ea73b8bdbe939457fa5ccb2c8152c22988ff5445b201fedee6e5f3611caab","last_reissued_at":"2026-05-18T02:13:46.183340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:46.183340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Denis Gaidashev, Tomas Johnson","submitted_at":"2009-05-09T09:33:41Z","abstract_excerpt":"It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\\fR}^2$. A renormalization approach has been used in \\cite{EKW1} and \\cite{EKW2} in a computer-assisted proof of existence of a \"universal\" area-preserving map $F_*$ -- a map with orbits of all binary periods $2^k, k \\in \\fN$. In this paper, we consider maps in some neighbourhood of $F_*$ and study their dynamics.\n  We first demonstrate that the map $F_*$ admits a \"bi-infinite heteroclinic tangle\": a sequence of periodic points $\\{z_k\\}$, $k \\in \\fZ$, |z_k| \\conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1390","kind":"arxiv","version":4},"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":"0905.1390","created_at":"2026-05-18T02:13:46.183484+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.1390v4","created_at":"2026-05-18T02:13:46.183484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.1390","created_at":"2026-05-18T02:13:46.183484+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMHKOO4L3PUT","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMHKOO4L3PUTSRL7","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMHKOO4L","created_at":"2026-05-18T12:25:59.703012+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/EMHKOO4L3PUTSRL7UXGLFSAVFQ","json":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ.json","graph_json":"https://pith.science/api/pith-number/EMHKOO4L3PUTSRL7UXGLFSAVFQ/graph.json","events_json":"https://pith.science/api/pith-number/EMHKOO4L3PUTSRL7UXGLFSAVFQ/events.json","paper":"https://pith.science/paper/EMHKOO4L"},"agent_actions":{"view_html":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ","download_json":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ.json","view_paper":"https://pith.science/paper/EMHKOO4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.1390&json=true","fetch_graph":"https://pith.science/api/pith-number/EMHKOO4L3PUTSRL7UXGLFSAVFQ/graph.json","fetch_events":"https://pith.science/api/pith-number/EMHKOO4L3PUTSRL7UXGLFSAVFQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ/action/storage_attestation","attest_author":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ/action/author_attestation","sign_citation":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ/action/citation_signature","submit_replication":"https://pith.science/pith/EMHKOO4L3PUTSRL7UXGLFSAVFQ/action/replication_record"}},"created_at":"2026-05-18T02:13:46.183484+00:00","updated_at":"2026-05-18T02:13:46.183484+00:00"}