{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T03:09:11Z","timestamp":1648523351846},"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> The global behavior of nonlinear systems is extremely important in control and systems theory since the usual local theories will only provide information about a system in some neighborhood of an operating point. Away from that point, the system may have totally different behavior and so the theory developed for the local system will be useless for the global one. <\/jats:p><jats:p> In this paper we shall consider the analytical and topological structure of systems on two- and three-manifolds and show that it is possible to obtain systems with \"arbitrarily strange\" behavior, i.e. arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries. <\/jats:p>","DOI":"10.1142\/s0218127407018233","type":"journal-article","created":{"date-parts":[[2007,9,4]],"date-time":"2007-09-04T11:33:08Z","timestamp":1188905588000},"page":"2085-2095","source":"Crossref","is-referenced-by-count":1,"title":["DYNAMICAL SYSTEMS ON THREE MANIFOLDS PART II: THREE-MANIFOLDS, <i>HEEGAARD SPLITTINGS<\/i> AND THREE-DIMENSIONAL SYSTEMS"],"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"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004152"},{"key":"rf2","author":"Banks S. P.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"rf3","volume-title":"3-Manifolds","author":"Hempel J.","year":"1976"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2307\/1970373"},{"key":"rf5","volume":"177","author":"Lozano M. T.","journal-title":"Pacific J. Math."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/9789812811172"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407018233","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:58:14Z","timestamp":1565189894000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407018233"}},"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\/S0218127407018233"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407018233","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6]]}}}