{"paper":{"title":"Hamiltonian vector fields of homogeneous polynomials in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2007-09-16T20:30:00Z","abstract_excerpt":"Let $g:\\mathbb{R}^2\\to\\mathbb{R}$ be a homogeneous polynomial of degree $p>1$, $G=(-g'_{y}, g'_{x})$ be its Hamiltonian vector field, and $G_t$ be the local flow generated by $G$. Denote by $E(G,O)$ the space of germs of $C^{\\infty}$ diffeomorphisms $(\\mathbb{R}^2,O)\\to(\\mathbb{R}^2,O)$ that preserve orbits of $G$. Let also $E_{\\mathrm{id}}(G,O)$ be the identity component of $E(G,O)$ with respect to $C^1$-topology.\n  Suppose that $g$ has no multiple prime factors. Then we prove that for every $h\\in E_{\\mathrm{id}}(G,O)$ there exists a germ of a smooth function $\\alpha:\\mathbb{R}^2\\to\\mathbb{R}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2511","kind":"arxiv","version":3},"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"}