{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T20:00:20Z","timestamp":1774468820980,"version":"3.50.1"},"reference-count":13,"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":[[2004,8]]},"abstract":"<jats:p> In this paper we present a relationship between the algebraic notion of proper system, the geometric notion of contact point and the dynamic notion of Poincar\u00e9 map for piecewise linear differential systems. This allows to present sufficient conditions (which are also necessary under additional hypotheses) for the existence of Poincar\u00e9 maps in piecewise linear differential systems. Moreover, an adequate parametrization of the Poincar\u00e9 maps make such maps invariant under linear transformations. <\/jats:p>","DOI":"10.1142\/s0218127404010874","type":"journal-article","created":{"date-parts":[[2004,9,17]],"date-time":"2004-09-17T10:44:54Z","timestamp":1095417894000},"page":"2843-2851","source":"Crossref","is-referenced-by-count":20,"title":["EXISTENCE OF POINCAR\u00c9 MAPS IN PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN \u211d<sup>N<\/sup>"],"prefix":"10.1142","volume":"14","author":[{"given":"JAUME","family":"LLIBRE","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat  Aut\u00f2noma de Barcelona, 08913 Bellaterra, Barcelona, Spain"}]},{"given":"ANTONIO E.","family":"TERUEL","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques i  Inform\u00e0tica, Edifici Anselm Turmeda, Universitat de les  Illes Balears, 07122 Palma, Spain"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Theory of Oscillators","author":"Andronov A.","year":"1987"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2002.1001950"},{"key":"rf4","volume-title":"Linear System Theory and Design","author":"Chen C. T.","year":"1984"},{"key":"rf5","first-page":"885","volume":"7","author":"Chua L. O.","journal-title":"IEEE Trans. Circuits Syst. CAS\u201337"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001728"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167913"},{"key":"rf9","volume-title":"Stability of Nonlinear Control Systems","author":"Lefschetz S.","year":"1965"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(95)00129-J"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(98)00175-8"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1109\/JRPROC.1962.288235"},{"key":"rf13","volume-title":"Frequency Domain Criteria for Absolute Stability","author":"Narendra K. S.","year":"1973"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749600045X"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127404010874","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:03:55Z","timestamp":1565136235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127404010874"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":13,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2004,8]]}},"alternative-id":["10.1142\/S0218127404010874"],"URL":"https:\/\/doi.org\/10.1142\/s0218127404010874","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}