{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:12:08Z","timestamp":1753884728313,"version":"3.41.2"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p> First, we study the planar continuous piecewise differential systems separated by the straight line [Formula: see text] formed by a linear isochronous center in [Formula: see text] and an isochronous quadratic center in [Formula: see text]. We prove that these piecewise differential systems cannot have crossing periodic orbits, and consequently they do not have crossing limit cycles. <\/jats:p><jats:p> Second, we study the crossing periodic orbits and limit cycles of the planar continuous piecewise differential systems separated by the straight line [Formula: see text] having in [Formula: see text] the general quadratic isochronous center [Formula: see text], [Formula: see text] after an affine transformation, and in [Formula: see text] an arbitrary quadratic isochronous center. For these kind of continuous piecewise differential systems the maximum number of crossing limit cycles is one, and there are examples having one crossing limit cycles. <\/jats:p><jats:p> In short for these families of continuous piecewise differential systems we have solved the extension of the 16th Hilbert problem. <\/jats:p>","DOI":"10.1142\/s0218127422500031","type":"journal-article","created":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T11:35:28Z","timestamp":1643024128000},"source":"Crossref","is-referenced-by-count":1,"title":["Limit Cycles of Continuous Piecewise Differential Systems Formed by Linear and Quadratic Isochronous Centers I"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0617-9665","authenticated-orcid":false,"given":"Bilal","family":"Ghermoul","sequence":"first","affiliation":[{"name":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria"}]},{"given":"Jaume","family":"Llibre","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"Tayeb","family":"Salhi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria"}]}],"member":"219","published-online":{"date-parts":[[2022,1,24]]},"reference":[{"key":"S0218127422500031BIB002","series-title":"Applied Mathematical Sciences","volume-title":"Piecewise-Smooth Dynamical Systems","volume":"163","author":"di Bernardo M.","year":"2008"},{"key":"S0218127422500031BIB003","first-page":"230","volume":"32","author":"Dulac H.","year":"1908","journal-title":"Bull. Sci. Math. S\u00e9r. (2)"},{"doi-asserted-by":"publisher","key":"S0218127422500031BIB007","DOI":"10.1090\/S0273-0979-02-00946-1"},{"key":"S0218127422500031BIB008","first-page":"21","volume":"3","author":"Li J.","year":"1964","journal-title":"Contrib. Diff. Eqs."},{"doi-asserted-by":"publisher","key":"S0218127422500031BIB009","DOI":"10.1142\/S0218127403006352"},{"doi-asserted-by":"publisher","key":"S0218127422500031BIB010","DOI":"10.1007\/s11071-015-2223-x"},{"doi-asserted-by":"publisher","key":"S0218127422500031BIB011","DOI":"10.1007\/s11071-017-3866-6"},{"key":"S0218127422500031BIB013","volume":"1","author":"Poincar\u00e9 H.","year":"1928","journal-title":"Oevres Compl\u00e8tes"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127422500031","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T11:37:13Z","timestamp":1643024233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127422500031"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":8,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1142\/S0218127422500031"],"URL":"https:\/\/doi.org\/10.1142\/s0218127422500031","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2022,1]]},"article-number":"2250003"}}