{"paper":{"title":"Image of a shift map along the orbits of a flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2009-02-14T00:37:58Z","abstract_excerpt":"Let $(F_t)$ be a smooth flow on a smooth manifold $M$ and $h:M\\to M$ be a smooth orbit preserving map. The following problem is studied: suppose that for every point $z$ of $M$ there exists a germ of a smooth function $f_z$ at $z$ such that near $z$ we have that $h(x)=F_{f_z(x)}(x)$. Can the functions $(f_z)$ be glued together to give a smooth function on all of $M$? This question is closely related to reparametrizations of flows. We describe a large class of flows for which the above problem can be resolved, and show that they have the following property: any smooth flow $(G_t)$ whose orbits "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2418","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"}