{"paper":{"title":"Global isochronous potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.DS","authors_text":"Gaetano Zampieri, Gianluca Gorni","submitted_at":"2012-05-01T16:13:53Z","abstract_excerpt":"We present a geometric characterization of the nonlinear smooth functions $V: R\\to R$ for which the origin is a global isochronous center for the scalar equation $\\ddot x=-V'(x)$. We revisit Stillinger and Dorignac isochronous potentials $V$ and show a new simple explicit family. Implicit examples are easily produced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0204","kind":"arxiv","version":7},"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"}