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We define $n$-ordered empirical measure of $x\\in X$ by \\begin{align*} \\mathscr{E}_n(x)=\\frac{1}{n}\\sum\\limits_{i=0}^{n-1}\\delta_{f^ix}, \\end{align*} where $\\delta_y$ is the Dirac mass at $y$. Denote by $V(x)$ the set of limit measures of the sequence of measures $\\mathscr{E}_n(x).$ In this paper, we obtain conditional variational principles for the topological entropy of \\begin{align*} \\Delta_{sub}(I)=\\left\\{x\\in X:V(x)\\subset I\\right\\}, \\end{align*} and \\begin{align*} \\"},"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":"1610.09106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-28T08:00:50Z","cross_cats_sorted":[],"title_canon_sha256":"0174189fe1a110ab06c959e32c00080d1415a82824270780472813fafefe4cd9","abstract_canon_sha256":"76490b8f5d929f1d761749d0d6d132a1a38061452bab6c4f39cbf5024a40620b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:59.115058Z","signature_b64":"EDuFue2XGSYxHGAOkZq/0ZvGTljCPNyIMM7pC9nZ4SIHad/657th74sLedgWsoW6ERC3TZb4t6EdWEuyiFTjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47347dcf8e9c231ee468957718eb22cbf29079a03654ae58c6168fc0a2b893ac","last_reissued_at":"2026-05-18T01:00:59.114448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:59.114448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Conditional Variational Principle for Maps with the Pseudo-orbit Tracing Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ercai Chen, Zheng Yin","submitted_at":"2016-10-28T08:00:50Z","abstract_excerpt":"Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\\in X$ by \\begin{align*} \\mathscr{E}_n(x)=\\frac{1}{n}\\sum\\limits_{i=0}^{n-1}\\delta_{f^ix}, \\end{align*} where $\\delta_y$ is the Dirac mass at $y$. Denote by $V(x)$ the set of limit measures of the sequence of measures $\\mathscr{E}_n(x).$ In this paper, we obtain conditional variational principles for the topological entropy of \\begin{align*} \\Delta_{sub}(I)=\\left\\{x\\in X:V(x)\\subset I\\right\\}, \\end{align*} and \\begin{align*} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09106","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":"1610.09106","created_at":"2026-05-18T01:00:59.114528+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09106v1","created_at":"2026-05-18T01:00:59.114528+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09106","created_at":"2026-05-18T01:00:59.114528+00:00"},{"alias_kind":"pith_short_12","alias_value":"I42H3T4OTQRR","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I42H3T4OTQRR5ZDI","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I42H3T4O","created_at":"2026-05-18T12:30:22.444734+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/I42H3T4OTQRR5ZDISV3RR2ZCZP","json":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP.json","graph_json":"https://pith.science/api/pith-number/I42H3T4OTQRR5ZDISV3RR2ZCZP/graph.json","events_json":"https://pith.science/api/pith-number/I42H3T4OTQRR5ZDISV3RR2ZCZP/events.json","paper":"https://pith.science/paper/I42H3T4O"},"agent_actions":{"view_html":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP","download_json":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP.json","view_paper":"https://pith.science/paper/I42H3T4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09106&json=true","fetch_graph":"https://pith.science/api/pith-number/I42H3T4OTQRR5ZDISV3RR2ZCZP/graph.json","fetch_events":"https://pith.science/api/pith-number/I42H3T4OTQRR5ZDISV3RR2ZCZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP/action/storage_attestation","attest_author":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP/action/author_attestation","sign_citation":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP/action/citation_signature","submit_replication":"https://pith.science/pith/I42H3T4OTQRR5ZDISV3RR2ZCZP/action/replication_record"}},"created_at":"2026-05-18T01:00:59.114528+00:00","updated_at":"2026-05-18T01:00:59.114528+00:00"}