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TitleDecomposition of algebraic sets and applications to weak centers of cubic systems
Author(s) Xuemin Chen, Weinian Zhang
TypeArticle in Journal
AbstractThere are many methods such as Gröbner basis, characteristic set and resultant, in computing an algebraic set of a system of multivariate polynomials. The common difficulties come from the complexity of computation, singularity of the corresponding matrices and some unnecessary factors in successive computation. In this paper, we decompose algebraic sets, stratum by stratum, into a union of constructible sets with Sylvester resultants, so as to simplify the procedure of elimination. Applying this decomposition to systems of multivariate polynomials resulted from period constants of reversible cubic differential systems which possess a quadratic isochronous center, we determine the order of weak centers and discuss the bifurcation of critical periods.
KeywordsAlgebraic set, Sylvester resultant, Reversible system, Weak center, Isochronous center, Bifurcation of critical periods
URL http://www.sciencedirect.com/science/article/pii/S0377042709003884
JournalJournal of Computational and Applied Mathematics
Pages565 - 581
Translation No
Refereed No