{"paper":{"title":"Discrete momentum maps for lattice EPDiff","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.NA","authors_text":"Colin J Cotter, Darryl D Holm","submitted_at":"2006-02-14T11:56:58Z","abstract_excerpt":"We focus on the spatial discretization produced by the Variational Particle-Mesh (VPM) method for a prototype fluid equation the known as the EPDiff equation}, which is short for Euler-Poincar\\'e equation associated with the diffeomorphism group (of $\\mathbb{R}^d$, or of a $d$-dimensional manifold $\\Omega$). The EPDiff equation admits measure valued solutions, whose dynamics are determined by the momentum maps for the left and right actions of the diffeomorphisms on embedded subspaces of $\\mathbb{R}^d$. The discrete VPM analogs of those dynamics are studied here. Our main results are: (i) a va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602296","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"}