{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AP4RV4B73SQQACBVWC4ZZSO437","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6f31e7b0a263eceb5e0b07248106690d306ec258b2ae061092eff36690b7f8c2","cross_cats_sorted":["math.PR","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-01T14:04:02Z","title_canon_sha256":"18c8092818e07121d50844346f6545c4b15b81112a1410df3466e3618a9678e7"},"schema_version":"1.0","source":{"id":"1007.0171","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0171","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0171v2","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0171","created_at":"2026-05-18T04:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"AP4RV4B73SQQ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AP4RV4B73SQQACBV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AP4RV4B7","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:7f3c24e40c9cd01caaaf36d3faaaf8c370ab48819a14df83c1f0b6b2ddf6a89d","target":"graph","created_at":"2026-05-18T04:12:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the number of visits to balls B_r(x), up to time t/mu(B_r(x)), for a class of non-uniformly hyperbolic dynamical systems, where mu is the SRB measure. Outside a set of `bad' centers x, we prove that this number is approximately Poissonnian with a controlled error term. In particular, when r-->0, we get convergence to the Poisson law for a set of centers of mu-measure one. Our theorem applies for instance to the H\\'enon attractor and, more generally, to systems modelled by a Young tower whose return-time function has a exponential tail and with one-dimensional unstable manifolds. Along","authors_text":"J.-R. Chazottes, P. Collet","cross_cats":["math.PR","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-01T14:04:02Z","title":"Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0171","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a7a4fd083374f259e5220783797685cbd68a83d98957dc702e57b10cc580d79f","target":"record","created_at":"2026-05-18T04:12:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f31e7b0a263eceb5e0b07248106690d306ec258b2ae061092eff36690b7f8c2","cross_cats_sorted":["math.PR","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-07-01T14:04:02Z","title_canon_sha256":"18c8092818e07121d50844346f6545c4b15b81112a1410df3466e3618a9678e7"},"schema_version":"1.0","source":{"id":"1007.0171","kind":"arxiv","version":2}},"canonical_sha256":"03f91af03fdca1000835b0b99cc9dcdfe948de36cd4f73768c61e39741938aeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03f91af03fdca1000835b0b99cc9dcdfe948de36cd4f73768c61e39741938aeb","first_computed_at":"2026-05-18T04:12:44.828438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:44.828438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tRytVEmr4qNU6YcuuZ6U/7WLFIOuLA5oBgG+rlF5b3yyItEv9LYiP0QmEvgW+lcaZ1Hg7Rn0Cj6vEJEFA5mcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:44.829241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0171","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7a4fd083374f259e5220783797685cbd68a83d98957dc702e57b10cc580d79f","sha256:7f3c24e40c9cd01caaaf36d3faaaf8c370ab48819a14df83c1f0b6b2ddf6a89d"],"state_sha256":"382a0aa254c1d4ebff57bc80f15afa75cd3d070906d6dbb4c10e156e4881359a"}