{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YS55DIXH3FWUZW5FVYDD7BMJ42","short_pith_number":"pith:YS55DIXH","schema_version":"1.0","canonical_sha256":"c4bbd1a2e7d96d4cdba5ae063f8589e69d3daa6127d34081b6cb781882705625","source":{"kind":"arxiv","id":"1504.05275","version":2},"attestation_state":"computed","paper":{"title":"Entropy, chaos and weak horseshoe for infinite dimensional random dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kening Lu, Wen Huang","submitted_at":"2015-04-21T02:00:34Z","abstract_excerpt":"In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a continuous random map has a positive topological entropy, then it contains a topological horseshoe. We also show that the positive topological entropy implies the chaos in the sense of Li-Yorke. The complicated behavior exhibiting here is induced by the positive entropy but not the randomness of the system."},"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":"1504.05275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-21T02:00:34Z","cross_cats_sorted":[],"title_canon_sha256":"641bd0f813d48d3db62b07cb6e85d60728929ee331d358cdae06ebdca3a24dc8","abstract_canon_sha256":"b3e1f8321110c615d3b31f27decfd9aae025d10822d899739f8190260910bcb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:44.691970Z","signature_b64":"IgBQvn4R+fc1smn87ztYlqdzNSBaAxYssXoGBM2lgu5NcqQqZXRbSgcKPGbqfl95IyS9hJWsLs0m/mUygfX8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4bbd1a2e7d96d4cdba5ae063f8589e69d3daa6127d34081b6cb781882705625","last_reissued_at":"2026-05-18T02:17:44.691562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:44.691562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy, chaos and weak horseshoe for infinite dimensional random dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kening Lu, Wen Huang","submitted_at":"2015-04-21T02:00:34Z","abstract_excerpt":"In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a continuous random map has a positive topological entropy, then it contains a topological horseshoe. We also show that the positive topological entropy implies the chaos in the sense of Li-Yorke. The complicated behavior exhibiting here is induced by the positive entropy but not the randomness of the system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05275","kind":"arxiv","version":2},"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":"1504.05275","created_at":"2026-05-18T02:17:44.691620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05275v2","created_at":"2026-05-18T02:17:44.691620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05275","created_at":"2026-05-18T02:17:44.691620+00:00"},{"alias_kind":"pith_short_12","alias_value":"YS55DIXH3FWU","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YS55DIXH3FWUZW5F","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YS55DIXH","created_at":"2026-05-18T12:29:52.810259+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/YS55DIXH3FWUZW5FVYDD7BMJ42","json":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42.json","graph_json":"https://pith.science/api/pith-number/YS55DIXH3FWUZW5FVYDD7BMJ42/graph.json","events_json":"https://pith.science/api/pith-number/YS55DIXH3FWUZW5FVYDD7BMJ42/events.json","paper":"https://pith.science/paper/YS55DIXH"},"agent_actions":{"view_html":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42","download_json":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42.json","view_paper":"https://pith.science/paper/YS55DIXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05275&json=true","fetch_graph":"https://pith.science/api/pith-number/YS55DIXH3FWUZW5FVYDD7BMJ42/graph.json","fetch_events":"https://pith.science/api/pith-number/YS55DIXH3FWUZW5FVYDD7BMJ42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42/action/storage_attestation","attest_author":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42/action/author_attestation","sign_citation":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42/action/citation_signature","submit_replication":"https://pith.science/pith/YS55DIXH3FWUZW5FVYDD7BMJ42/action/replication_record"}},"created_at":"2026-05-18T02:17:44.691620+00:00","updated_at":"2026-05-18T02:17:44.691620+00:00"}