{"paper":{"title":"Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Piero Negrini, Sergey Bolotin","submitted_at":"2013-08-21T14:53:10Z","abstract_excerpt":"We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\\mu>0$ shadowing chains of homoclinic orbits to $M$ are represented as extremals of a discrete variational problem, and their existence is proved. This paper is motivated by applications to the Poincar\\'e second species solutions of the 3 body problem with 2 masses small of order $\\mu$. As $\\mu\\to 0$, double collisions of small bodies correspond to a symplectic critical manifold of the regularized Hamilto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4604","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"}