华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (3): 169-175.

• 应用数学与基础数学 • 上一篇    下一篇

{${\bm t}$-${\bm P}$-${\mathcal{\bm K}}$-等价的隐函数定理与余维估计

许静波1,  陈 亮2,  孙伟志3   

  1. 1. 吉林师范大学~~数学学院, 吉林~~四平 136000; 2. 东北师范大学~~数学与统计学院, 长春 130024; 3. 长春理工大学~~理学院, 长春 130022
  • 收稿日期:2012-09-01 修回日期:2012-12-01 出版日期:2013-05-25 发布日期:2013-07-10

Implicit function theorem and codimension estimation relative to ${\bm t}$-${\bm P}$-${\mathcal{K}}$-equivalence

XU Jing-bo1,  CHEN Liang2,  SUN Wei-zhi3   

  1. 1. School of Mathematics, Jilin Normal University, Siping Jilin 136000, China; 2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China; 3. College of Science, Changchun University of Science and Technology, Changchun 130022, China
  • Received:2012-09-01 Revised:2012-12-01 Online:2013-05-25 Published:2013-07-10

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摘要： 证得光滑映射芽在\,${t}$-${P}$-${\mathcal{K}}$-等价关系下的隐函数定理,
并对其余维进行估计.
所得结果可为对具有区别参数的光滑映射芽的分类研究提供有力工具,
也可成为讨论完全可积微分方程芽分支的基础.

关键词: 光滑映射芽, $t$-$P$-${\mathcal{K}}$-等价, 隐函数定理, 余维

Abstract: The implicit function theorem under
$t$-$P$-${\mathcal{K}}$-equivalence relation was obtained, and the
$t$-$P$-${\mathcal{K}}$-codimension was also estimated. The result
may be a powerful tool for the classification of smooth mapping
germs with distinguished parameters relative to
$t$-$P$-${\mathcal{K}}$-equivalence, and for the study of
bifurcations of differential equation germs with complete integral.

Key words: smooth map germ, $t$-$P$-${\mathcal{K}}$-equivalence, implicit function theorem, codimension

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