{"paper":{"title":"Choreographies in the $n$-vortex problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Garc\\'ia-Azpeitia, Eusebius Doedel, Renato Calleja","submitted_at":"2018-07-21T23:44:26Z","abstract_excerpt":"We consider the equations of motion of $n$ vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference. We use numerical continuation in a boundary value setting to determine the Lyapunov families of periodic orbits that arise from the polygonal relative equilibrium. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship then the orbit is also periodic in the inertial frame. A dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08212","kind":"arxiv","version":2},"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"}