{"paper":{"title":"Geometry of slow-fast Hamiltonian systems and Painlev\\'e equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"E.I. Yakovlev, L.M. Lerman","submitted_at":"2015-11-26T17:22:26Z","abstract_excerpt":"In the first part of the paper we introduce some geometric tools needed to describe slow-fast Hamiltonian systems on smooth manifolds. We start with a smooth Poisson bundle $p: M\\to B$ of a regular (i.e. of constant rank) Poisson manifold $(M,\\omega)$ over a smooth symplectic manifold $(B,\\lambda)$, the foliation into leaves of the bundle coincides with the symplectic foliation generated by the Poisson structure on $M$. This defines a singular symplectic structure $\\Omega_{\\varepsilon}=$ $\\omega + \\varepsilon^{-1}p^*\\lambda$ on $M$ for any positive small $\\varepsilon$, where $p^*\\lambda$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08454","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"}