Journal of East China Normal University(Natural Sc ›› 2013, Vol. 2013 ›› Issue (3): 169-175.

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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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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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