Details:
Title  Decomposition of algebraic sets and applications to weak centers of cubic systems  Author(s)  Xuemin Chen, Weinian Zhang  Type  Article in Journal  Abstract  There 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.  Keywords  Algebraic set, Sylvester resultant, Reversible system, Weak center, Isochronous center, Bifurcation of critical periods  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S0377042709003884 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  232  Number  2  Pages  565  581  Year  2009  Edition  0  Translation 
No  Refereed 
No 
