{"paper":{"title":"Variational approach to second species periodic solutions of Poincar\\'e of the 3 body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Piero Negrini, Sergey Bolotin","submitted_at":"2011-04-12T18:00:41Z","abstract_excerpt":"We consider the plane 3 body problem with 2 of the masses small. Periodic solutions with near collisions of small bodies were named by Poincar\\'e second species periodic solutions. Such solutions shadow chains of collision orbits of 2 uncoupled Kepler problems. Poincar\\'e only sketched the proof of the existence of second species solutions. Rigorous proofs appeared much later and only for the restricted 3 body problem. We develop a variational approach to the existence of second species periodic solutions for the nonrestricted 3 body problem. As an application, we give a rigorous proof of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2288","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"}