{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DTR5S4HX3EAM6EFE25PBESTIAI","short_pith_number":"pith:DTR5S4HX","schema_version":"1.0","canonical_sha256":"1ce3d970f7d900cf10a4d75e124a68022f7d5f802044a04610f7d26f745e00ed","source":{"kind":"arxiv","id":"1406.0208","version":1},"attestation_state":"computed","paper":{"title":"Cubic perturbations of elliptic Hamiltonian vector fields of degree three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Iliya D. Iliev, Lubomir Gavrilov","submitted_at":"2014-06-01T21:26:37Z","abstract_excerpt":"The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $X_\\varepsilon$ $$ X_\\varepsilon : \\left\\{ \\begin{array}{llr} \\dot{x}=\\;\\; H_y+\\varepsilon f(x,y)\\\\ \\dot{y}=-H_x+\\varepsilon g(x,y), \\end{array} \\;\\;\\;\\;\\; H~=\\frac{1}{2} y^2~+U(x)\n  \\right. $$ which bifurcate from the period annuli of $X_0$ for sufficiently small $\\varepsilon$. Here $U$ is a univariate polynomial of degree four without symmetry, and $f, g$ are arbitrary cubic polynomials in two variables.\n  We take a period annulus and parameterize the related displacement m"},"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":"1406.0208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-01T21:26:37Z","cross_cats_sorted":[],"title_canon_sha256":"5e4a12d061712e8fc78b60ac44cc63ac2a603aa0f57c7950df51537a615f22fe","abstract_canon_sha256":"e963550a37731bdf2141737fa4e3bafe389760dddb2c7faf60670649fa0ece14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.528772Z","signature_b64":"h0GkG52wC6jSo64DObfru3GcOSLAt9Qn3LP62HkXOWLAGwAoac3khw5bWXnrgE1isQQjNTIvJNEWNi1Ue+abCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ce3d970f7d900cf10a4d75e124a68022f7d5f802044a04610f7d26f745e00ed","last_reissued_at":"2026-05-18T02:50:41.528237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.528237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cubic perturbations of elliptic Hamiltonian vector fields of degree three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Iliya D. Iliev, Lubomir Gavrilov","submitted_at":"2014-06-01T21:26:37Z","abstract_excerpt":"The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $X_\\varepsilon$ $$ X_\\varepsilon : \\left\\{ \\begin{array}{llr} \\dot{x}=\\;\\; H_y+\\varepsilon f(x,y)\\\\ \\dot{y}=-H_x+\\varepsilon g(x,y), \\end{array} \\;\\;\\;\\;\\; H~=\\frac{1}{2} y^2~+U(x)\n  \\right. $$ which bifurcate from the period annuli of $X_0$ for sufficiently small $\\varepsilon$. Here $U$ is a univariate polynomial of degree four without symmetry, and $f, g$ are arbitrary cubic polynomials in two variables.\n  We take a period annulus and parameterize the related displacement m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0208","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":"1406.0208","created_at":"2026-05-18T02:50:41.528311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0208v1","created_at":"2026-05-18T02:50:41.528311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0208","created_at":"2026-05-18T02:50:41.528311+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTR5S4HX3EAM","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTR5S4HX3EAM6EFE","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTR5S4HX","created_at":"2026-05-18T12:28:25.294606+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/DTR5S4HX3EAM6EFE25PBESTIAI","json":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI.json","graph_json":"https://pith.science/api/pith-number/DTR5S4HX3EAM6EFE25PBESTIAI/graph.json","events_json":"https://pith.science/api/pith-number/DTR5S4HX3EAM6EFE25PBESTIAI/events.json","paper":"https://pith.science/paper/DTR5S4HX"},"agent_actions":{"view_html":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI","download_json":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI.json","view_paper":"https://pith.science/paper/DTR5S4HX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0208&json=true","fetch_graph":"https://pith.science/api/pith-number/DTR5S4HX3EAM6EFE25PBESTIAI/graph.json","fetch_events":"https://pith.science/api/pith-number/DTR5S4HX3EAM6EFE25PBESTIAI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI/action/storage_attestation","attest_author":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI/action/author_attestation","sign_citation":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI/action/citation_signature","submit_replication":"https://pith.science/pith/DTR5S4HX3EAM6EFE25PBESTIAI/action/replication_record"}},"created_at":"2026-05-18T02:50:41.528311+00:00","updated_at":"2026-05-18T02:50:41.528311+00:00"}