{"paper":{"title":"Topological approach to the generalized $n$-center problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergey Bolotin, Valery Kozlov","submitted_at":"2017-05-12T17:39:11Z","abstract_excerpt":"We consider a natural Hamiltonian system with two degrees of freedom and Hamiltonian $H=\\|p\\|^2/2+V(q)$. The configuration space $M$ is a closed surface (for noncompact $M$ certain conditions at infinity are required). It is well known that if the potential energy $V$ has $n>2\\chi(M)$ Newtonian singularities, then the system is not integrable and has positive topological entropy on energy levels $H=h>\\sup V$. We generalize this result to the case when the potential energy has several singular points $a_j$ of type $V(q)\\sim -d(q,a_j)^{-\\alpha_j}$. Let $A_k=2-2k^{-1}$, $k=2,3,\\dots$, and let $n_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04671","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"}