{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5363F6NSWKDODCM5KDD4SACA7M","short_pith_number":"pith:5363F6NS","schema_version":"1.0","canonical_sha256":"eefdb2f9b2b286e1899d50c7c90040fb06f574ca9874dc309de384665248812d","source":{"kind":"arxiv","id":"1112.4686","version":1},"attestation_state":"computed","paper":{"title":"Towards a renormalization theory for quasi-periodically forced one dimensional maps II. Asymptotic behavior of reducibility loss bifurcations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Angel Jorba, Joan Carles Tatjer, Pau Rabassa","submitted_at":"2011-12-20T13:50:02Z","abstract_excerpt":"In this paper we are concerned with quasi-periodic forced one dimensional maps. We consider a two parametric family of quasi-periodically forced maps such that the one dimensional map (before forcing) is unimodal and it has a full cascade of period doubling bifurcations. Between one period doubling and the next one it is known that there exist a parameter value where the $2^n$-periodic orbit is superatracting. In a previous work we proposed an extension of the one-dimensional (doubling) renormalization operator to the quasi-periodic case. We proved that, if the family satisfies suitable hypoth"},"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":"1112.4686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-12-20T13:50:02Z","cross_cats_sorted":[],"title_canon_sha256":"f60d7e9bc88cbfd346e59d56fedf0a06b2890f70107a26879e1b18f465fa70a7","abstract_canon_sha256":"94d7e06a9689e213e8541d9c25832022e5b99a687f04607f088a963e63ce6bf5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:58.248921Z","signature_b64":"NNuM/WZV+slFP6P2Tk/3+P5qZdXVSUoqeqxkvF7KSrEQ74ld8/fKSZNG7MkrrkvyUUXLLQeQ4Y+goNWdnX5DDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eefdb2f9b2b286e1899d50c7c90040fb06f574ca9874dc309de384665248812d","last_reissued_at":"2026-05-18T04:05:58.248233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:58.248233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards a renormalization theory for quasi-periodically forced one dimensional maps II. Asymptotic behavior of reducibility loss bifurcations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Angel Jorba, Joan Carles Tatjer, Pau Rabassa","submitted_at":"2011-12-20T13:50:02Z","abstract_excerpt":"In this paper we are concerned with quasi-periodic forced one dimensional maps. We consider a two parametric family of quasi-periodically forced maps such that the one dimensional map (before forcing) is unimodal and it has a full cascade of period doubling bifurcations. Between one period doubling and the next one it is known that there exist a parameter value where the $2^n$-periodic orbit is superatracting. In a previous work we proposed an extension of the one-dimensional (doubling) renormalization operator to the quasi-periodic case. We proved that, if the family satisfies suitable hypoth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4686","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":"1112.4686","created_at":"2026-05-18T04:05:58.248353+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.4686v1","created_at":"2026-05-18T04:05:58.248353+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4686","created_at":"2026-05-18T04:05:58.248353+00:00"},{"alias_kind":"pith_short_12","alias_value":"5363F6NSWKDO","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5363F6NSWKDODCM5","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5363F6NS","created_at":"2026-05-18T12:26:20.644004+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/5363F6NSWKDODCM5KDD4SACA7M","json":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M.json","graph_json":"https://pith.science/api/pith-number/5363F6NSWKDODCM5KDD4SACA7M/graph.json","events_json":"https://pith.science/api/pith-number/5363F6NSWKDODCM5KDD4SACA7M/events.json","paper":"https://pith.science/paper/5363F6NS"},"agent_actions":{"view_html":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M","download_json":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M.json","view_paper":"https://pith.science/paper/5363F6NS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.4686&json=true","fetch_graph":"https://pith.science/api/pith-number/5363F6NSWKDODCM5KDD4SACA7M/graph.json","fetch_events":"https://pith.science/api/pith-number/5363F6NSWKDODCM5KDD4SACA7M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M/action/storage_attestation","attest_author":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M/action/author_attestation","sign_citation":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M/action/citation_signature","submit_replication":"https://pith.science/pith/5363F6NSWKDODCM5KDD4SACA7M/action/replication_record"}},"created_at":"2026-05-18T04:05:58.248353+00:00","updated_at":"2026-05-18T04:05:58.248353+00:00"}