{"paper":{"title":"Positive-entropy Hamiltonian systems on Nilmanifolds via Scattering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"Leo T. Butler","submitted_at":"2014-02-10T12:16:41Z","abstract_excerpt":"Let $\\Sigma$ be a compact quotient of $T_4$, the Lie group of $4 \\times 4$ upper triangular matrices with unity along the diagonal. The Lie algebra $t_4$ of $T_4$ has the standard basis $\\{X_{ij}\\}$ of matrices with $0$ everywhere but in the $(i,j)$ entry, which is unity. Let $g$ be the Carnot metric, a sub-riemannian metric, on $T_4$ for which $X_{i,i+1}$, $(i=1,2,3)$, is an orthonormal basis. Montgomery, Shapiro and Stolin showed that the geodesic flow of $g$ is algebraically non-integrable. This note proves that the geodesic flow of that Carnot metric on $T \\Sigma$ has positive topological "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2122","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"}