{"paper":{"title":"Saari's Conjecture and Variational Minimal Solutions for $N$-Body Problems","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Yu Xiang, Zhang Shiqing","submitted_at":"2013-06-05T10:26:14Z","abstract_excerpt":"In this paper, we will prove Saari's conjecture in a particular case by using a arithmetic fact, and then, apply it to prove that for any given positive masses, the variational minimal solutions of the N-body problem in ${\\mathbb{R}}^2$ are precisely a relative equilibrium solution whose configuration minimizes the function $IU^2$ in ${{\\mathbb{R}}}^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1047","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"}