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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 $Sh=E_{\\mathrm{id"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0708.0737","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-08-06T10:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"6c7e75a2d4a11b4b79ce99c38ca779d913cffa840b2d2826928ce8ee469702b7","abstract_canon_sha256":"4763a72ffc685ad461f63c15737ed8cc8880be7ced6e10ed30d00c501fa0206d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:48.614614Z","signature_b64":"0sOWDecooVHcGJaqTD5nTbiWkf3tdnDFcSrGlLhYMrs6lyqif4tOkJSSixrUQXn7g+Sw+ZHB2yIEQCtRbXwTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b8ee612fb62c7e271402f1d37b569a009e8bb95bf0db0488890efde88efe071","last_reissued_at":"2026-05-18T01:23:48.614052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:48.614052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\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. 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