{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:27:08Z","timestamp":1772267228296,"version":"3.50.1"},"reference-count":34,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T00:00:00Z","timestamp":1598313600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[2020,11]]},"abstract":"<jats:p>We describe topological obstructions (involving periodic points, topological entropy and rotation sets) for a homeomorphism on a compact manifold to embed in a continuous flow. We prove that homeomorphisms in a<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0013091520000280_inline1.png\"\/><jats:tex-math>$C^{0}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-open and dense set of homeomorphisms isotopic to the identity in compact manifolds of dimension at least two are not the time-1 map of a continuous flow. Such property is also true for volume-preserving homeomorphisms in compact manifolds of dimension at least five. In the case of conservative homeomorphisms of the torus<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0013091520000280_inline2.png\"\/><jats:tex-math>$\\mathbb {T}^{d} (d\\ge 2)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>isotopic to identity, we describe necessary conditions for a homeomorphism to be flowable in terms of the rotation sets.<\/jats:p>","DOI":"10.1017\/s0013091520000280","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T03:21:22Z","timestamp":1598325682000},"page":"971-983","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["Continuous flows generate few homeomorphisms"],"prefix":"10.1017","volume":"63","author":[{"given":"Wescley","family":"Bonomo","sequence":"first","affiliation":[]},{"given":"Paulo","family":"Varandas","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,8,25]]},"reference":[{"key":"S0013091520000280_ref16","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2015.1063620"},{"key":"S0013091520000280_ref24","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1974-13470-1"},{"key":"S0013091520000280_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2018.06.002"},{"key":"S0013091520000280_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/1970228"},{"key":"S0013091520000280_ref3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1965-11304-0"},{"key":"S0013091520000280_ref34","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0076436"},{"key":"S0013091520000280_ref10","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-66-03348-5"},{"key":"S0013091520000280_ref15","doi-asserted-by":"crossref","unstructured":"15. 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