{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MF3DWVPOJ75M3JVL5WOBRKNF2X","short_pith_number":"pith:MF3DWVPO","schema_version":"1.0","canonical_sha256":"61763b55ee4ffacda6abed9c18a9a5d5fecbaae5ebc3f6c85d92a46b2022d1f1","source":{"kind":"arxiv","id":"1511.08648","version":1},"attestation_state":"computed","paper":{"title":"Dynamics of conservative Bykov cycles: tangencies, generalized cocoon bifurcations and elliptic solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre Rodrigues, Mario Bessa","submitted_at":"2015-11-27T12:41:01Z","abstract_excerpt":"This paper presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a conservative Bykov cycle where trajectories turn in opposite directions near the two saddle-foci. We show that {within the class of divergence-free vector fields that preserve the cycle,} tangencies of the invariant manifolds of two hyperbolic saddle-foci densely occur. The global dynamics is persistently dominated by heteroclinic tangencies and by the existence of infinitely many elliptic points coexisting with suspended hyperbolic horseshoes. A generalized version of "},"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":"1511.08648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-27T12:41:01Z","cross_cats_sorted":[],"title_canon_sha256":"1b0dbeb62f8d27b64d4ccf9a39de4ee213e59995061ad84a32afe883334ac5a3","abstract_canon_sha256":"df90edc8ea776cfa8bce0e389aff7f14a9dc5051562f4a08b4764e274bef425a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:48.410115Z","signature_b64":"dHC5fvwwey0Qa0VFO3Fxw21lYj3MOMlIhXmYT3PJNUTEgE/RqB8x2ZXXhxw4zxipsRsHcmMJ1UrWHmTiBkMGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61763b55ee4ffacda6abed9c18a9a5d5fecbaae5ebc3f6c85d92a46b2022d1f1","last_reissued_at":"2026-05-18T01:25:48.409622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:48.409622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of conservative Bykov cycles: tangencies, generalized cocoon bifurcations and elliptic solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre Rodrigues, Mario Bessa","submitted_at":"2015-11-27T12:41:01Z","abstract_excerpt":"This paper presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a conservative Bykov cycle where trajectories turn in opposite directions near the two saddle-foci. We show that {within the class of divergence-free vector fields that preserve the cycle,} tangencies of the invariant manifolds of two hyperbolic saddle-foci densely occur. The global dynamics is persistently dominated by heteroclinic tangencies and by the existence of infinitely many elliptic points coexisting with suspended hyperbolic horseshoes. A generalized version of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08648","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":"1511.08648","created_at":"2026-05-18T01:25:48.409688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08648v1","created_at":"2026-05-18T01:25:48.409688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08648","created_at":"2026-05-18T01:25:48.409688+00:00"},{"alias_kind":"pith_short_12","alias_value":"MF3DWVPOJ75M","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MF3DWVPOJ75M3JVL","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MF3DWVPO","created_at":"2026-05-18T12:29:32.376354+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/MF3DWVPOJ75M3JVL5WOBRKNF2X","json":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X.json","graph_json":"https://pith.science/api/pith-number/MF3DWVPOJ75M3JVL5WOBRKNF2X/graph.json","events_json":"https://pith.science/api/pith-number/MF3DWVPOJ75M3JVL5WOBRKNF2X/events.json","paper":"https://pith.science/paper/MF3DWVPO"},"agent_actions":{"view_html":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X","download_json":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X.json","view_paper":"https://pith.science/paper/MF3DWVPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08648&json=true","fetch_graph":"https://pith.science/api/pith-number/MF3DWVPOJ75M3JVL5WOBRKNF2X/graph.json","fetch_events":"https://pith.science/api/pith-number/MF3DWVPOJ75M3JVL5WOBRKNF2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X/action/storage_attestation","attest_author":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X/action/author_attestation","sign_citation":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X/action/citation_signature","submit_replication":"https://pith.science/pith/MF3DWVPOJ75M3JVL5WOBRKNF2X/action/replication_record"}},"created_at":"2026-05-18T01:25:48.409688+00:00","updated_at":"2026-05-18T01:25:48.409688+00:00"}