{"paper":{"title":"Generating hyperbolic singularities in completely integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.SG"],"primary_cat":"math-ph","authors_text":"\\'Alvaro Pelayo, Holger R. Dullin","submitted_at":"2015-03-05T04:25:58Z","abstract_excerpt":"Let $(M,\\Omega)$ be a connected symplectic 4-manifold and let $F=(J,H) : M \\to \\mathbb{R}^2$ be a completely integrable system on $M$ with only non-degenerate singularities and for which $J : M \\to \\mathbb{R}$ is a proper map. Assume that $F$ does not have singularities with hyperbolic blocks and that $p_1,...,p_n$ are the focus-focus singularities of $F$. For each subset $S=\\{i_1,...,i_j\\}$ we will show how to modify $F$ locally around any $p_i, i \\in S$, in order to create a new integrable system $\\tilde{F}=(J, \\tilde{H}) : M \\to \\mathbb{R}^2$ such that its classical spectrum $\\tilde{F}(M)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01534","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"}