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Define $E_{x}(f, y) := E(f, y) \\cap W^u(x)$ for any $x\\in M$. Following a method of Broderick-Fishman-Kleinbock, we show that $E_x(f,y)$ is a winning set of Schmidt games played on $W^u(x)$ which implies that $E_x(f,y)$ has full Hausdorff dimension equal to $\\dim W^u(x)$. Furthermore we show that for any nonempty open set $V \\subset M$, $E(f, y) \\cap "},"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":"1311.5309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-21T04:24:49Z","cross_cats_sorted":[],"title_canon_sha256":"7603eac03069dd172f8ed89a45897e069b51a2815313340e3645c44e30999f9e","abstract_canon_sha256":"2a1813d521edc8d35aa4d8925205f275634cd95ee48170d7cbc2a0f468b4fd0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:33.717258Z","signature_b64":"GySzNSig8QMs210E3/KMqCdaoAcP0MJJl0vQH6StkN9oESQ5OjBTXoAHCiVvzA/1HUi1dGlNU+Xiyvy64q36Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8555a7e0e7ff9f3bfb948666d6dd16e4384db314188f33706f2ce109f7f319e5","last_reissued_at":"2026-05-18T03:06:33.716605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:33.716605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schmidt Games and Nondense forward Orbits of certain Partially Hyperbolic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weisheng Wu","submitted_at":"2013-11-21T04:24:49Z","abstract_excerpt":"Let $f: M \\to M$ be a partially hyperbolic diffeomorphism with conformality on unstable manifolds. Consider a set of points with nondense forward orbit: $E(f, y) := \\{ z\\in M: y\\notin \\overline{\\{f^k(z), k \\in \\mathbb{N}\\}}\\}$ for some $y \\in M$. Define $E_{x}(f, y) := E(f, y) \\cap W^u(x)$ for any $x\\in M$. Following a method of Broderick-Fishman-Kleinbock, we show that $E_x(f,y)$ is a winning set of Schmidt games played on $W^u(x)$ which implies that $E_x(f,y)$ has full Hausdorff dimension equal to $\\dim W^u(x)$. Furthermore we show that for any nonempty open set $V \\subset M$, $E(f, y) \\cap "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5309","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":"1311.5309","created_at":"2026-05-18T03:06:33.716715+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.5309v1","created_at":"2026-05-18T03:06:33.716715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5309","created_at":"2026-05-18T03:06:33.716715+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVK2PYHH76PT","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVK2PYHH76PTX64U","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVK2PYHH","created_at":"2026-05-18T12:27:57.521954+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/QVK2PYHH76PTX64UQZTNNXIW4Q","json":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q.json","graph_json":"https://pith.science/api/pith-number/QVK2PYHH76PTX64UQZTNNXIW4Q/graph.json","events_json":"https://pith.science/api/pith-number/QVK2PYHH76PTX64UQZTNNXIW4Q/events.json","paper":"https://pith.science/paper/QVK2PYHH"},"agent_actions":{"view_html":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q","download_json":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q.json","view_paper":"https://pith.science/paper/QVK2PYHH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.5309&json=true","fetch_graph":"https://pith.science/api/pith-number/QVK2PYHH76PTX64UQZTNNXIW4Q/graph.json","fetch_events":"https://pith.science/api/pith-number/QVK2PYHH76PTX64UQZTNNXIW4Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q/action/storage_attestation","attest_author":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q/action/author_attestation","sign_citation":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q/action/citation_signature","submit_replication":"https://pith.science/pith/QVK2PYHH76PTX64UQZTNNXIW4Q/action/replication_record"}},"created_at":"2026-05-18T03:06:33.716715+00:00","updated_at":"2026-05-18T03:06:33.716715+00:00"}