{"paper":{"title":"Symplectic integrators in the realm of Hofer's geometry","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":"2011-12-31T05:08:27Z","abstract_excerpt":"Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a \"sourrounded\" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on the time by h. When the numerical integration of a Hamiltonian system involves more than one symplectic scheme as in the parallel-in-time algorithms, there are not a simple way to control the dynamical behavior of the error Hamiltonian. The interplay of to different symplectic integrators can degenerate their behavior if both have different dynamical propertie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0225","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"}