{"paper":{"title":"Scattering parabolic solutions for the spatial N-centre problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alberto Boscaggin, Susanna Terracini, Walter Dambrosio","submitted_at":"2016-02-09T08:36:01Z","abstract_excerpt":"For the $N$-centre problem in the three dimensional space, $$ \\ddot x = -\\sum_{i=1}^{N} \\frac{m_i \\,(x-c_i)}{\\vert x - c_i \\vert^{\\alpha+2}}, \\qquad x \\in \\mathbb{R}^3 \\setminus \\{c_1,\\ldots,c_N\\}, $$ where $N \\geq 2$, $m_i > 0$ and $\\alpha \\in [1,2)$, we prove the existence of entire parabolic trajectories having prescribed asymptotic directions. The proof relies on a variational argument of min-max type. Morse index estimates and regularization techniques are used in order to rule out the possible occurrence of collisions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02897","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"}