{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PEJTPBMSXXXGRA3YT72ONCIUQG","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":"de932a8647d836a1fbd4f4c628faf827ae70252353a318460d2dc58cba8786c9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-28T02:54:30Z","title_canon_sha256":"0d50ebe282baa07bff873350908e02c0cebaaedea0304fea4c2b9d6d85b5d7aa"},"schema_version":"1.0","source":{"id":"1011.6011","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6011","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6011v3","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6011","created_at":"2026-05-18T01:26:25Z"},{"alias_kind":"pith_short_12","alias_value":"PEJTPBMSXXXG","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PEJTPBMSXXXGRA3Y","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PEJTPBMS","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:a80271dac45812e9254eb585fd1a5fdf3083570ee231e65d34dae5836cb396e8","target":"graph","created_at":"2026-05-18T01:26:25Z","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":"In this paper we consider a non-atomic invariant hyperbolic measure $\\mu$ of a $C^1$ diffeomorphsim on a compact manifold, in whose Oseledec splitting the stable bundle dominates the unstable bundle on $\\mu$ a.e. points. We show an \\textit{exponentially} shadowing and an \\textit{exponentially} closing lemma, and as applications we show two classical results. One is that there exists a hyperbolic periodic point such that the closure of its unstable manifold has \\textit{positive} measure and it has a homoclinic point from which one can deduce a horseshoe. Moreover, such hyperbolic periodic point","authors_text":"Xueting Tian","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-28T02:54:30Z","title":"Hyperbolic Periodic Points and Hyperbolic Measures with Dominated Splitting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6011","kind":"arxiv","version":3},"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:d289ba9bd18bf6411d70e3098bc6a2a5f388cccc25dfbe092133833dd861cb08","target":"record","created_at":"2026-05-18T01:26:25Z","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":"de932a8647d836a1fbd4f4c628faf827ae70252353a318460d2dc58cba8786c9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-28T02:54:30Z","title_canon_sha256":"0d50ebe282baa07bff873350908e02c0cebaaedea0304fea4c2b9d6d85b5d7aa"},"schema_version":"1.0","source":{"id":"1011.6011","kind":"arxiv","version":3}},"canonical_sha256":"7913378592bdee6883789ff4e6891481b42d46fb1248fd151bb67e348403825e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7913378592bdee6883789ff4e6891481b42d46fb1248fd151bb67e348403825e","first_computed_at":"2026-05-18T01:26:25.812349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:25.812349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ryZW0NMU4V72PwaDqFD9EHiaM+p9m4GoVyFefk38fBT7TAo2oetqgvkeEILQ81iM14X1owdFHe6HxJ1FW9kgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:25.812751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6011","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d289ba9bd18bf6411d70e3098bc6a2a5f388cccc25dfbe092133833dd861cb08","sha256:a80271dac45812e9254eb585fd1a5fdf3083570ee231e65d34dae5836cb396e8"],"state_sha256":"c5039dfe6c8960d270f6c08dd97e429bec9aaf187972bd60f361b80b8a1f8481"}