{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T11:59:27Z","timestamp":1774267167624,"version":"3.50.1"},"reference-count":16,"publisher":"Elsevier BV","issue":"5","license":[{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3766,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2003,5]]},"DOI":"10.1016\/s0747-7171(03)00016-6","type":"journal-article","created":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T14:33:56Z","timestamp":1049726036000},"page":"577-589","source":"Crossref","is-referenced-by-count":26,"title":["The Sibirsky component of the center variety of polynomial differential systems"],"prefix":"10.1016","volume":"35","author":[{"given":"Abdul Salam","family":"Jarrah","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reinhard","family":"Laubenbacher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valery","family":"Romanovski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0747-7171(03)00016-6_B1","series-title":"An Introduction to Gr\u00f6bner Bases","volume":"vol. 3","author":"Adams","year":"1994"},{"key":"10.1016\/S0747-7171(03)00016-6_B2","series-title":"Local Theory of Nonlinear Analytic Ordinary Differential Equations","volume":"vol. 702","author":"Bibikov","year":"1979"},{"key":"10.1016\/S0747-7171(03)00016-6_B3","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1216\/rmjm\/1181071923","article-title":"Algebraic properties of the Lyapunov and periodic constants","volume":"27","author":"Cima","year":"1997","journal-title":"Rocky Mountain J. Math."},{"key":"10.1016\/S0747-7171(03)00016-6_B4","first-page":"230","article-title":"D\u00e9t\u00e9rmination et int\u00e9gration d\u2019une certaine classe d\u2019\u00e9quations diff\u00e9rentielles ayant pour point singulier un centre","volume":"32","author":"Dulac","year":"1908","journal-title":"Bull. Sci. Math."},{"key":"10.1016\/S0747-7171(03)00016-6_B5","unstructured":"Grayson, D., Stillman, M., Macaulay2: a Software System for Algebraic Geometry. Available from http:\/\/www.math.uiuc.edu\/Macaulay2"},{"key":"10.1016\/S0747-7171(03)00016-6_B6","unstructured":"Reyn, J., 1994. A bibliography of the qualitative theory of quadratic systems of differential equations in the plane, third edn., Report 94\u201302. Delft University of Technology"},{"key":"10.1016\/S0747-7171(03)00016-6_B7","first-page":"782","article-title":"On a calculation of Lyapunov focus quantities in the case of two imaginary roots","volume":"29","author":"Romanovski","year":"1993","journal-title":"Differ. Equ."},{"key":"10.1016\/S0747-7171(03)00016-6_B8","doi-asserted-by":"crossref","first-page":"10267","DOI":"10.1088\/0305-4470\/34\/47\/326","article-title":"The center and isochronicity problems for some cubic systems","volume":"34","author":"Romanovski","year":"2001","journal-title":"J. Phys. A: Math. Gen."},{"key":"10.1016\/S0747-7171(03)00016-6_B9","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1006\/jdeq.1995.1168","article-title":"Cubic vector fields symmetric with respect to a center","volume":"123","author":"Rousseau","year":"1995","journal-title":"J. Differential Equations"},{"key":"10.1016\/S0747-7171(03)00016-6_B10","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1090\/S0002-9947-1993-1106193-6","article-title":"Algebraic particular integrals, integrability and the problem of the center","volume":"338","author":"Schlomiuk","year":"1993","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0747-7171(03)00016-6_B11","series-title":"Algebraic Invariants of Differential Equations and Matrices","author":"Sibirsky","year":"1976"},{"key":"10.1016\/S0747-7171(03)00016-6_B12","series-title":"Introduction to the Algebraic Theory of Invariants of Differential Equations","author":"Sibirsky","year":"1988"},{"key":"10.1016\/S0747-7171(03)00016-6_B13","series-title":"Algorithms in Invariant Theory","author":"Sturmfels","year":"1993"},{"key":"10.1016\/S0747-7171(03)00016-6_B14","series-title":"Gr\u00f6bner Bases and Convex Polytopes","volume":"vol. 8","author":"Sturmfels","year":"1998"},{"key":"10.1016\/S0747-7171(03)00016-6_B15","first-page":"10","article-title":"Theory of values of singular point in complex autonomous differential systems","volume":"30","author":"Yi-Rong","year":"1989","journal-title":"Sci. China Ser. A"},{"key":"10.1016\/S0747-7171(03)00016-6_B16","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1006\/jdeq.1997.3260","article-title":"The problem of center for resonant singular points of polynomial vector fields","volume":"137","author":"\u017bo\u0142a\u0327dek","year":"1997","journal-title":"J. Differential Equations"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717103000166?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717103000166?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,24]],"date-time":"2019-03-24T12:29:48Z","timestamp":1553430588000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717103000166"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":16,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2003,5]]}},"alternative-id":["S0747717103000166"],"URL":"https:\/\/doi.org\/10.1016\/s0747-7171(03)00016-6","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2003,5]]}}}