{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T12:48:33Z","timestamp":1762865313319},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:p> In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a system containing the braids and extending periodically to obtain a system naturally defined on a torus and which contains the given knotted trajectories. To get explicit differential equations for dynamical systems containing the braids, we will use a certain function to define a tube neighborhood of the braid. The second one, generating chaotic systems, is realized by modeling the Smale horseshoe. <\/jats:p>","DOI":"10.1142\/s0218127407018221","type":"journal-article","created":{"date-parts":[[2007,9,4]],"date-time":"2007-09-04T11:33:08Z","timestamp":1188905588000},"page":"2073-2084","source":"Crossref","is-referenced-by-count":2,"title":["DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART I: KNOTS, LINKS AND CHAOS"],"prefix":"10.1142","volume":"17","author":[{"given":"YI","family":"SONG","sequence":"first","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]},{"given":"STEPHEN P.","family":"BANKS","sequence":"additional","affiliation":[{"name":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"}]},{"given":"DAVID","family":"DIAZ","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":"10.1007\/BF02950724"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404009776"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015209"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(83)90045-9"},{"key":"rf5","series-title":"LNM","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0093387","volume-title":"Knots and Links in Three-Dimensional Flows","volume":"1654","author":"Ghrist R. W.","year":"1997"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/1116"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407018221","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:58:12Z","timestamp":1565189892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407018221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6]]},"references-count":6,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,6]]}},"alternative-id":["10.1142\/S0218127407018221"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407018221","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6]]}}}