{"paper":{"title":"A Separating Surface for Sitnikov-like n+1-body Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lennard Bakker, Skyler Simmons","submitted_at":"2014-10-09T21:36:18Z","abstract_excerpt":"We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless particle on the z-axis. The study of the motion of this particle can then be modelled as a time-dependent Hamiltonian System. We give a geometric construction of a surface in the three-dimensional phase space separating orbits for which the massless particle escapes to infinity from those for which it does not. The construction is demonstrated numerically in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2636","kind":"arxiv","version":3},"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"}