{"paper":{"title":"$\\infty$-jets of difeomorphisms preserving orbits of vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2007-08-06T10:26:00Z","abstract_excerpt":"Let $F$ be a smooth vector field defined in a neighborhood of the origin in $\\mathbb{R}^n$, $F(O)=0$, and let $F_t$ be its local flow. Denote by $E$ the set of germs of diffeomorphisms $h:\\mathbb{R}^n \\to \\mathbb{R}^n$ preserving orbits of $F$ and let $E_{\\mathrm{id}}^r$ be the identity component of $E$ with respect to $C^r$-topology. Then every $E_{\\mathrm{id}}^{r}$ contains a subset $Sh$ consisting of mappings of the form $F_{f(x)}(x)$, where $f: \\mathbb{R}^n \\to \\mathbb{R}$ is a smooth function. It was proved earlier by the author that if $F$ is a linear vector field, then $Sh=E_{\\mathrm{id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0737","kind":"arxiv","version":7},"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"}