{"paper":{"title":"A property of conformally Hamiltonian vector fields; application to the Kepler problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Charles-Michel Marle","submitted_at":"2010-11-26T08:56:14Z","abstract_excerpt":"Let $X$ be a Hamiltonian vector field defined on a symplectic manifold $(M,\\omega)$, $g$ a nowhere vanishing smooth function defined on an open dense subset $M^0$ of $M$. We will say that the vector field $Y = gX$ is conformally Hamiltonian. We prove that when $X$ is complete, when $Y$ is Hamiltonian with respect to another symplectic form $\\omega_2$ defined on $M^0$, and when another technical condition is satisfied, there exists a symplectic diffeomorphism from $(M^0,\\omega_2)$ onto an open subset of $(M,\\omega)$, equivariant with respect to the flows of the vector fields $Y$ on $M^0$ and $X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5731","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"}