Symbolic computation and the cyclicity problem for singularities
Symbolic computation and the cyclicity problem for singularities
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DOI：
10.1016/j.jsc.2011.12.037
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
D. Shafer
中科院分区：
文献类型：
--
作者：
D. Shafer
我们展示了如何采用计算交换代数方法来研究局部第 16 希尔伯特问题，即找到可以从 R2 上的微分方程组多项式系统族中的奇点分叉的极限环数量的上限，并且是解决完整第 16 希尔伯特问题的程序中的一个步骤。我们讨论一个著名定理的扩展，并用具体例子说明概念和方法。
We show how methods of computational commutative algebra are employed to investigate the local 16th Hilbert Problem, which is to find an upper bound on the number of limit cycles that can bifurcate from singularities in families of polynomial systems of differential equations on R2, and is one step in a program for solving the full 16th Hilbert Problem. We discuss an extension of a well-known theorem, and illustrate the concepts and methods with concrete examples.