{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T11:14:57Z","timestamp":1768734897658,"version":"3.49.0"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,10]]},"abstract":"<jats:p> In this paper by using the Poincar\u00e9 compactification of \u211d<jats:sup>3<\/jats:sup> we describe the global dynamics of the Lorenz system [Formula: see text] having some invariant algebraic surfaces. Of course (x, y, z) \u2208 \u211d<jats:sup>3<\/jats:sup> are the state variables and (s, r, b) \u2208 \u211d<jats:sup>3<\/jats:sup> are the parameters. For six sets of the parameter values, the Lorenz system has invariant algebraic surfaces. For these six sets, we provide the global phase portrait of the system in the Poincar\u00e9 ball (i.e. in the compactification of \u211d<jats:sup>3<\/jats:sup> with the sphere \ud835\udd4a<jats:sup>2<\/jats:sup> of the infinity). <\/jats:p>","DOI":"10.1142\/s0218127410027593","type":"journal-article","created":{"date-parts":[[2010,11,3]],"date-time":"2010-11-03T08:12:33Z","timestamp":1288771953000},"page":"3137-3155","source":"Crossref","is-referenced-by-count":45,"title":["GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES"],"prefix":"10.1142","volume":"20","author":[{"given":"JAUME","family":"LLIBRE","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"MARCELO","family":"MESSIAS","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e3o, Faculdade de Ci\u00eancias e Tecnologia, UNESP \u2013 Univ Estadual Paulista, Cx. Postal 266, 19060-900, Presidente Prudente, S\u00e3o Paulo, Brazil"}]},{"given":"PAULO RICARDO","family":"DA SILVA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto de Bioci\u00eancias, Letras e Ci\u00eancias Exatas, UNESP \u2013 Univ Estadual Paulista, Rua C. Colombo, 2265, 15054\u2013000, S. J. Rio Preto, S\u00e3o Paulo, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"1","volume":"48","author":"Cao J.","journal-title":"J. Math. Phys."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0998352-5"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/19\/12\/013"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1063\/1.166450"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/030600180"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/17\/1\/000"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1063\/1.1435078"},{"key":"rf8","first-page":"21pp","volume":"41","author":"Llibre J.","journal-title":"J. Phys. A: Math. Theoret."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"rf10","first-page":"18pp","volume":"42","author":"Messias M.","journal-title":"J. Phys. A: Math. Theoret."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(02)00136-X"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5767-7"},{"key":"rf13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1017\/S0305004101005667","volume":"132","author":"Swinnerton-Dyer P.","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF03025276"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127410027593","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:54:58Z","timestamp":1565135698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127410027593"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10]]},"references-count":14,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2010,10]]}},"alternative-id":["10.1142\/S0218127410027593"],"URL":"https:\/\/doi.org\/10.1142\/s0218127410027593","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10]]}}}