{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:GK5DUDIQN5MPTESOSUSVP5J5RN","short_pith_number":"pith:GK5DUDIQ","schema_version":"1.0","canonical_sha256":"32ba3a0d106f58f9924e952557f53d8b50e2637658218c97372b8fe1f137e563","source":{"kind":"arxiv","id":"0901.0574","version":3},"attestation_state":"computed","paper":{"title":"Lorenz like flows: exponential decay of correlations for the Poincar\\'e map, logarithm law, quantitative recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"M. J. Pacifico, S. Galatolo","submitted_at":"2009-01-05T23:23:31Z","abstract_excerpt":"In this paper we prove that the Poincar\\'e map associated to a Lorenz like flow has exponential decay of correlations with respect to Lipschitz observables. This implies that the hitting time associated to the flow satisfies a logarithm law. The hitting time $\\tau_r(x,x_0)$ is the time needed for the orbit of a point $x$ to enter for the first time in a ball $B_r(x_0)$ centered at $x_0$, with small radius $r$. As the radius of the ball decreases to 0 its asymptotic behavior is a power law whose exponent is related to the local dimension of the SRB measure at $x_0$: for each $x_0$ such that the"},"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":"0901.0574","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-05T23:23:31Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"196aa740915e0e1b778d3c4e7e358480b214d164e4002ea04c0fd2d51d65da92","abstract_canon_sha256":"39248a50f69202459f782c5cdffe1c59cf9abb394f32189bfa388cbed4502470"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:46:05.690761Z","signature_b64":"fyjyaV0/RlTetEefWotgVl2TdBLKrHRgbZJzMUxh2L1Sa3foV+DfSgCiN8N1KJXqM8rTRPxUT5iNnXp5U2FRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32ba3a0d106f58f9924e952557f53d8b50e2637658218c97372b8fe1f137e563","last_reissued_at":"2026-07-04T15:46:05.690365Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:46:05.690365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lorenz like flows: exponential decay of correlations for the Poincar\\'e map, logarithm law, quantitative recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"M. J. Pacifico, S. Galatolo","submitted_at":"2009-01-05T23:23:31Z","abstract_excerpt":"In this paper we prove that the Poincar\\'e map associated to a Lorenz like flow has exponential decay of correlations with respect to Lipschitz observables. This implies that the hitting time associated to the flow satisfies a logarithm law. The hitting time $\\tau_r(x,x_0)$ is the time needed for the orbit of a point $x$ to enter for the first time in a ball $B_r(x_0)$ centered at $x_0$, with small radius $r$. As the radius of the ball decreases to 0 its asymptotic behavior is a power law whose exponent is related to the local dimension of the SRB measure at $x_0$: for each $x_0$ such that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0574","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0901.0574/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0901.0574","created_at":"2026-07-04T15:46:05.690435+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.0574v3","created_at":"2026-07-04T15:46:05.690435+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0574","created_at":"2026-07-04T15:46:05.690435+00:00"},{"alias_kind":"pith_short_12","alias_value":"GK5DUDIQN5MP","created_at":"2026-07-04T15:46:05.690435+00:00"},{"alias_kind":"pith_short_16","alias_value":"GK5DUDIQN5MPTESO","created_at":"2026-07-04T15:46:05.690435+00:00"},{"alias_kind":"pith_short_8","alias_value":"GK5DUDIQ","created_at":"2026-07-04T15:46:05.690435+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/GK5DUDIQN5MPTESOSUSVP5J5RN","json":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN.json","graph_json":"https://pith.science/api/pith-number/GK5DUDIQN5MPTESOSUSVP5J5RN/graph.json","events_json":"https://pith.science/api/pith-number/GK5DUDIQN5MPTESOSUSVP5J5RN/events.json","paper":"https://pith.science/paper/GK5DUDIQ"},"agent_actions":{"view_html":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN","download_json":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN.json","view_paper":"https://pith.science/paper/GK5DUDIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.0574&json=true","fetch_graph":"https://pith.science/api/pith-number/GK5DUDIQN5MPTESOSUSVP5J5RN/graph.json","fetch_events":"https://pith.science/api/pith-number/GK5DUDIQN5MPTESOSUSVP5J5RN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN/action/storage_attestation","attest_author":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN/action/author_attestation","sign_citation":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN/action/citation_signature","submit_replication":"https://pith.science/pith/GK5DUDIQN5MPTESOSUSVP5J5RN/action/replication_record"}},"created_at":"2026-07-04T15:46:05.690435+00:00","updated_at":"2026-07-04T15:46:05.690435+00:00"}