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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_"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.04671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-12T17:39:11Z","cross_cats_sorted":[],"title_canon_sha256":"67310317248894b3ff55a4b107e3c7337b07397593d33b08791a9d2919e0e8f1","abstract_canon_sha256":"1a4014bceeb46546d61bd52560ac331cf8066e28301c4a1d889b6ec87f312332"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:37.517079Z","signature_b64":"SnGohX2HdYPjFMFZlXL215rdkPuilPUc7zs5dAno/B6zGizf+PBCNa7zPRKbV5Js+EmIph9vInfVlttiI7zrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eae69dfbcbf3543914c7285e3ce810cc658b8fc11f852191fcc5e89ac838e617","last_reissued_at":"2026-05-18T00:44:37.516627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:37.516627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $H=\\|p\\|^2/2+V(q)$. 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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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.04671","created_at":"2026-05-18T00:44:37.516697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.04671v1","created_at":"2026-05-18T00:44:37.516697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04671","created_at":"2026-05-18T00:44:37.516697+00:00"},{"alias_kind":"pith_short_12","alias_value":"5LTJ366L6NKD","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5LTJ366L6NKDSFGH","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5LTJ366L","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR","json":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR.json","graph_json":"https://pith.science/api/pith-number/5LTJ366L6NKDSFGHFBPDZ2AQZR/graph.json","events_json":"https://pith.science/api/pith-number/5LTJ366L6NKDSFGHFBPDZ2AQZR/events.json","paper":"https://pith.science/paper/5LTJ366L"},"agent_actions":{"view_html":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR","download_json":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR.json","view_paper":"https://pith.science/paper/5LTJ366L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.04671&json=true","fetch_graph":"https://pith.science/api/pith-number/5LTJ366L6NKDSFGHFBPDZ2AQZR/graph.json","fetch_events":"https://pith.science/api/pith-number/5LTJ366L6NKDSFGHFBPDZ2AQZR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR/action/storage_attestation","attest_author":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR/action/author_attestation","sign_citation":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR/action/citation_signature","submit_replication":"https://pith.science/pith/5LTJ366L6NKDSFGHFBPDZ2AQZR/action/replication_record"}},"created_at":"2026-05-18T00:44:37.516697+00:00","updated_at":"2026-05-18T00:44:37.516697+00:00"}