{"paper":{"title":"Reparametrizations of vector fields and their shift maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2009-07-02T12:07:08Z","abstract_excerpt":"Let $M$ be a smooth manifold, $F$ be a smooth vector field on $M$, and $F_t$ be the local flow of $F$. Denote by $Sh(F)$ the space of smooth maps $h:M\\to M$ of the following form: $h(x) = F_{f(x)}(x)$, where $f:M\\to\\mathbb{R}$ runs over all smooth functions on $M$ which can be substituted into the flow $F_t$ instead of time. This space often coincides with the identity component of the group of diffeomorphisms preserving orbits of $F$. In this note it is shown that $Sh(F)$ is not changed under reparametrizations and pushforwards of $F$. As an application it is proved that a vector field $F$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0354","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"}