{"paper":{"title":"Reducing scattering problems under cone potentials to normal form by global canonical transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Gaetano Zampieri, Gianluca Gorni","submitted_at":"2012-04-07T14:08:23Z","abstract_excerpt":"We introduce a class of Hamiltonian scattering systems which can be reduced to the \"normal form\" $\\dot P=0$, $\\dot Q=P$, by means of a global canonical transformation $ (P,Q)=A(p,q), p,q\\in R^n$, defined through asymptotic properties of the trajectories.\n  These systems are obtained requiring certain geometrical conditions on $\\dot p=-\\nabla V(q)$, $\\dot q=p$, where $V$ is a bounded below \"cone potential\", i.e., the force $-\\nabla V(q)$ always belongs to a closed convex cone which contains no straight lines.\n  We can deal with very different asymptotic behaviours of the potential and the poten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1640","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"}