{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T11:46:55Z","timestamp":1648813615917},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2008,8]]},"abstract":"<jats:p> The main result of this paper is a proof of existence of a nontrivial knot on any embedded template, that was left as an open question to prove in [Ghrist et al., 1997] without using the Bennequin's inequality [Ghrist et al., 1997]. This result in the branched two-manifold case, which we prove by a sequence of lemmas showing our simple template (or ones with twists) containing nontrivial knots is (are) contained in every template as a subtemplate, enables us to generalize it later in this paper to certain forms of three-templates in four-dimensional dynamical systems by simply using the technique of \"spinning\" the knots in the lower dimensional templates to obtain the spun knotted surfaces. <\/jats:p>","DOI":"10.1142\/s0218127408021828","type":"journal-article","created":{"date-parts":[[2008,10,10]],"date-time":"2008-10-10T08:44:55Z","timestamp":1223628295000},"page":"2461-2470","source":"Crossref","is-referenced-by-count":3,"title":["BRANCHED MANIFOLDS, KNOTTED SURFACES AND DYNAMICAL SYSTEMS"],"prefix":"10.1142","volume":"18","author":[{"given":"W.","family":"CHEN","sequence":"first","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]},{"given":"S. P.","family":"BANKS","sequence":"additional","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(83)90045-9"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/020\/718132"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0093387"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082847"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/chel\/346"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127408021828","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:01:13Z","timestamp":1565136073000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127408021828"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8]]},"references-count":5,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,8]]}},"alternative-id":["10.1142\/S0218127408021828"],"URL":"https:\/\/doi.org\/10.1142\/s0218127408021828","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8]]}}}