开折的无穷小稳定性及其在分支问题中的应用  

The Infinitesimal Stability of Unfoldings and It's Applications to Bifurcation Problems

作　　者：邹建成[1] 李国富[1] 

机构地区：[1]北方工业大学基础科学学院,北京石景山100041

出　　处：《北方工业大学学报》1998年第1期5-11,共7页Journal of North China University of Technology

基　　金：国家自然科学基金!19771035;北方工业大学科研基金

摘　　要：文献[6]讨论了C∞映射芽关于群A的一个子群的万有开折性问题．本文给出了此子群之下开折无穷小稳定的条件，并利用这种思想，给出了分支问题无穷小稳定开折的定义，证明了它与分支问题的万有开折是等价的，从而得到一个判别万有开折的准则．In [6], the universal unfolding of C∞ map germs under a subgroup of A was discussed. In this paper, some conditions are given to characterize the infinitesimal stability of unfoldings under the same group. The definition of infinitesimal stability of unfolding of bifurcation problem is also defined. The equivalence of infinitesimal stability and universality of unfoldings of bifurcation problems is proved, then a direct criterion of universality of unfoldings of bifurcation problems is given.

关 键 词：开折 映射芽 万有开折 分支问题 无穷小稳定性 

分 类 号：O19[理学—数学]