奇点处分岔解支的数目问题*
On the Problem of the Number of Bifurcation Solutions at Singular Point
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摘要: 本文在孤立奇点的假设下证明了带参数非线性方程组解的孤立性,同时指出在分岔点处必有而且仅有有限条解支分岔出来．这一结论是分岔问题数值方法的一个理论基础．Abstract: In this paper,it is proved that the solutions of a nonlinear equation are isolated under Ihe condition that the singular points are isolated.It shows that there musl have and Only have finite solutions branching from bifurcation point.This is important.for the numerical analysis of bifurcation problems.
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Key words:
- homotopy /
- continuation method /
- bifurcation /
- isolated singularity
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[1] 季海波、武际可、胡海昌,分叉问题的几何描述及其计算方法,中国科学(A),(9)(1991),947. [2] E.Allgower and K.Georg-Numerical Continuation Methods,Springer-Verlag(1990). [3] S.N.Chow and J.K.Hale,Methods of Bifurcation Theory,Springer-Verlag(1982). [4] 武际可、苏先椒,《弹性系统的稳定性》,科学出版社(1994). -
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