{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T05:07:13Z","timestamp":1772428033636,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,11]]},"abstract":"<jats:p> Suppose that the differential system [Formula: see text] has a center at the origin for \u03b5=0, where P<jats:sub>0<\/jats:sub>, Q<jats:sub>0<\/jats:sub>, a<jats:sub>ij<\/jats:sub> and b<jats:sub>ij<\/jats:sub> are analytic functions in their variables, such that a<jats:sub>ij<\/jats:sub>(0)=b<jats:sub>ij<\/jats:sub>(0)=0. We present an analytic method to compute the semistable limit cycles which bifurcate from the periodic orbits of the analytic center, up to an arbitrary order in the perturbation parameter \u03b5. We also provide an algorithm for the computation of the saddle\u2013node bifurcation hypersurface of limit cycles in the parameter space {a<jats:sub>ij<\/jats:sub>,b<jats:sub>ij<\/jats:sub>}<jats:sub>1\u2264i,j\u2264m<\/jats:sub>. As an example, we apply the method to compute, first, the anal ytic expression of the unique semistable limit cycle of the Li\u00e9nard system [Formula: see text] and second, an approximation of the saddle-node bifurcation surface of limit cycles in the parameter space (a<jats:sub>1<\/jats:sub>, a<jats:sub>3<\/jats:sub>, a<jats:sub>5<\/jats:sub>). Both computations are valid for \u03b5 sufficiently small. <\/jats:p>","DOI":"10.1142\/s0218127403008600","type":"journal-article","created":{"date-parts":[[2003,12,18]],"date-time":"2003-12-18T09:02:05Z","timestamp":1071738125000},"page":"3489-3498","source":"Crossref","is-referenced-by-count":3,"title":["SEMISTABLE LIMIT CYCLES THAT BIFURCATE FROM CENTERS"],"prefix":"10.1142","volume":"13","author":[{"given":"HECTOR","family":"GIACOMINI","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Physique  Th\u00e9orique, CNRS (U.M.R. 6083), Facult\u00e9 des Sciences et Techniques, Universit\u00e9 de Tours, Parc de Grandmont, 37200 Tours, France"}]},{"given":"MIREILLE","family":"VIANO","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et Physique  Th\u00e9orique, CNRS (U.M.R. 6083), Facult\u00e9 des Sciences et Techniques, Universit\u00e9 de Tours, Parc de Grandmont, 37200 Tours, France"}]},{"given":"JAUME","family":"LLIBRE","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques,  Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra,  Barcelona, Spain"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Theory of Bifurcations of Dynamic Systems on a Plane","author":"Andronov A. 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Monographs","volume-title":"Qualitative Theory of Differential Equations","volume":"101","author":"Zhang Z.","year":"1992"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403008600","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:15:12Z","timestamp":1565136912000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403008600"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11]]},"references-count":13,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,11]]}},"alternative-id":["10.1142\/S0218127403008600"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403008600","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,11]]}}}