Decomposition of algebraic sets and applications to weak centers of cubic systems |
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Authors: | Xingwu Chen |
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Affiliation: | Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China |
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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. |
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Keywords: | Algebraic set Sylvester resultant Reversible system Weak center Isochronous center Bifurcation of critical periods |
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