{"paper":{"title":"Block-Separation of Variables: a Form of Partial Separation for Natural Hamiltonians","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Claudia Maria Chanu, Giovanni Rastelli","submitted_at":"2018-08-06T13:33:32Z","abstract_excerpt":"We study twisted products $H=\\alpha^rH_r$ of natural autonomous Hamiltonians $H_r$, each one depending on a separate set, called here separate $r$-block, of variables. We show that, when the twist functions $\\alpha^r$ are a row of the inverse of a block-St\\\"ackel matrix, the dynamics of $H$ reduces to the dynamics of the $H_r$, modified by a scalar potential depending only on variables of the corresponding $r$-block. It is a kind of partial separation of variables. We characterize this block-separation in an invariant way by writing in block-form classical results of St\\\"ackel separation of va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01889","kind":"arxiv","version":2},"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"}