{"paper":{"title":"Geometry of the discrete Hamilton--Jacobi equation. Applications in optimal control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"C. Sard\\'on, M. De Le\\'On","submitted_at":"2017-04-17T09:04:05Z","abstract_excerpt":"In this paper, we review the discrete Hamilton--Jacobi theory from a geometric point of view. In the discrete realm, the usual geometric interpretation of the Hamilton--Jacobi theory in terms of vector fields is not straightforward.\n  Here, we propose two alternative interpretations: one is the interpretation in terms of projective flows, the second is the temptative of constructing a discrete Hamiltonian vector field renacting the usual continuous interpretation.\n  Both interpretations are proven to be equivalent and applied in optimal control theory. The solutions achieved through both appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04907","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"}