{"paper":{"title":"Symplectic maps: from generating functions to Liouvillian forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.SG","authors_text":"Hugo Jim\\'enez-P\\'erez","submitted_at":"2015-08-13T15:37:22Z","abstract_excerpt":"In this article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way, the method of generating functions to 1-forms which are globally defined on the symplectic manifold. The maps constructed by this method, are related to the symplectic Cayley's transformation and belong to a continuous space of dimension n(2n+1). Applying the implicit map to the discrete Hamilton equations we obtain the generalized symplectic Euler scheme. We show the relations of the elements of this family with ot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03250","kind":"arxiv","version":4},"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"}