{"paper":{"title":"Morse index and bifurcation for figure-eight choreographies of the equal mass three-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Fukuda, Hiroshi Ozaki, Toshiaki Fujiwara","submitted_at":"2019-01-01T08:28:59Z","abstract_excerpt":"We report on the Morse index and periodic solutions bifurcating from the figure-eight choreography for the equal mass three-body problem under homogeneous potential $-1/r^a$ for $a \\ge 0$, and under Lennard-Jones (LJ) type potential $1/r^{12}-1/r^6$, where $r$ is a distance between bodies. It is shown that the Morse index changes at a bifurcation point and all solutions bifurcating are approximated by variational functions responsible for the change of the Morse index. Inversely we observed %numerically bifurcation occurs at every point where the Morse index changes for the figure-eight choreo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00115","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"}