{"paper":{"title":"Minimal $P$-symmetric period problem of first-order autonomous Hamiltonian Systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ben-Xing Zhou, Chungen Liu","submitted_at":"2016-12-13T05:26:04Z","abstract_excerpt":"Let $P\\in Sp(2n)$ satisfying $P^{k}=I_{2n}$, we consider the minimal $P$-symmetric period problem of the autonomous nonlinear Hamiltonian system\n  \\begin{equation*} \\dot x(t) = JH^{\\prime}(x(t)). \\end{equation*} For some symplectic matrices $P$, we show that for any $\\tau>0$ the above Hamiltonian system possesses a $k\\tau$ periodic solution $x$ with $k\\tau$ being its minimal $P$-symmetric period provided $H$ satisfies the Rabinowitz's conditions on the minimal period conjecture, together with that $H$ is convex and $H(Px)=H(x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04033","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"}