{"paper":{"title":"Blow-up for realizing homotopy classes in the three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Richard Montgomery","submitted_at":"2015-07-28T23:03:38Z","abstract_excerpt":"This expository note describes McGehee blow-up \\cite{McGehee} in its role as one of the main tools in my recent proof with Rick Moeckel \\cite{RM2} that every free homotopy class for the planar three-body problem can be realized by a periodic solution. The main novelty is my use of energy-balance to motivate the transformation of McGehee. Another novelty is an explicit description of the blown-up reduced phase space for the planar N-body problem, $N \\ge 3$ as a complex vector bundle over the half-line times complex projective $N-2$-space. The half line coordinate is the size of the labelled pla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07982","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"}