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As applications we study the minimal period problems for brake orbits of nonlinear autonomous reversible Hamiltonian systems. For first order nonlinear autonomous reversible Hamiltonian systems in $\\R^{2n}$, which are semipositive, and superquadratic at zero and infinity, we prove that for any $T>0$, the considered Hamiltonian systems possesses a nonconstant $T$ periodic brake "},"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":"1110.6915","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2011-10-31T19:43:26Z","cross_cats_sorted":[],"title_canon_sha256":"2bce4f783d125cdf10da902b180e247c1cd81e7af18a8d6040ceb5c2fc4b5329","abstract_canon_sha256":"c016f11b9c31ee976c4c66d686c7dfc67c71a3c41268de20368b239609a63e01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:53.907871Z","signature_b64":"PDyiXBQJXdnFD8NvfieV6DzxeqEGBgAUHGGqTnXH340Hz9kZCIbgI8GdUcNX/jxefdXbWEZDfAKRIjL+JsQmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c42e99a0815fa8ca821811d4d876a5dd2828f0fa22ef43523e3f6febaad4e77","last_reissued_at":"2026-05-18T04:09:53.907417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:53.907417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal period problems for brake orbits of nonlinear autonomous reversible semipositive Hamiltonian systems","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Duanzhi Zhang","submitted_at":"2011-10-31T19:43:26Z","abstract_excerpt":"In this paper, for any positive integer $n$, we study the Maslov-type index theory of $i_{L_0}$, $i_{L_1}$ and $i_{\\sqrt{-1}}^{L_0}$ with $L_0=\\{0\\}\\times \\R^n\\subset \\R^{2n}$ and $L_1=\\R^n\\times \\{0\\} \\subset \\R^{2n}$. As applications we study the minimal period problems for brake orbits of nonlinear autonomous reversible Hamiltonian systems. For first order nonlinear autonomous reversible Hamiltonian systems in $\\R^{2n}$, which are semipositive, and superquadratic at zero and infinity, we prove that for any $T>0$, the considered Hamiltonian systems possesses a nonconstant $T$ periodic brake "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6915","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":"1110.6915","created_at":"2026-05-18T04:09:53.907484+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6915v1","created_at":"2026-05-18T04:09:53.907484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6915","created_at":"2026-05-18T04:09:53.907484+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRBOTGQICX5I","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRBOTGQICX5IZKBB","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRBOTGQI","created_at":"2026-05-18T12:26:37.096874+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/NRBOTGQICX5IZKBBQEOU3B3KLX","json":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX.json","graph_json":"https://pith.science/api/pith-number/NRBOTGQICX5IZKBBQEOU3B3KLX/graph.json","events_json":"https://pith.science/api/pith-number/NRBOTGQICX5IZKBBQEOU3B3KLX/events.json","paper":"https://pith.science/paper/NRBOTGQI"},"agent_actions":{"view_html":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX","download_json":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX.json","view_paper":"https://pith.science/paper/NRBOTGQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6915&json=true","fetch_graph":"https://pith.science/api/pith-number/NRBOTGQICX5IZKBBQEOU3B3KLX/graph.json","fetch_events":"https://pith.science/api/pith-number/NRBOTGQICX5IZKBBQEOU3B3KLX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX/action/storage_attestation","attest_author":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX/action/author_attestation","sign_citation":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX/action/citation_signature","submit_replication":"https://pith.science/pith/NRBOTGQICX5IZKBBQEOU3B3KLX/action/replication_record"}},"created_at":"2026-05-18T04:09:53.907484+00:00","updated_at":"2026-05-18T04:09:53.907484+00:00"}