数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1411-1424.doi: 10.1016/S0252-9602(11)60327-5

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Cl -GV TRIVIALITY OF FUNCTION GERMS AND NEWTON POLYHEDRA

刘恒兴1,2|张敦穆1   

  1. 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
    2. College of Management, Beijing Normal University, Beijing 100875, China
  • 收稿日期:2009-07-21 出版日期:2011-07-20 发布日期:2011-07-20
  • 基金资助:

    This work was supported by the National Nature Science Foundation of China (10671009; 10871149).

Cl -GV TRIVIALITY OF FUNCTION GERMS AND NEWTON POLYHEDRA

 LIU Heng-Xing1,2, ZHANG Dun-Mu1   

  1. 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
    2. College of Management, Beijing Normal University, Beijing 100875, China
  • Received:2009-07-21 Online:2011-07-20 Published:2011-07-20
  • Supported by:

    This work was supported by the National Nature Science Foundation of China (10671009; 10871149).

摘要:

Weprovideestimates onthedegreeof Cl -GV determinacy(G is oneofMather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives lan explicit order such that the Cl geometrical structure of a function germ is preserved l after higher order perturbations, which generalizes the result on Cl-G triviality of function germs given by M.A.S.Ruas.

关键词: Cl -RV triviality, Cl-KV triviality, A-isolated, controlled vector field

Abstract:

Weprovideestimates onthedegreeof Cl -GV determinacy(G is oneofMather’s groups R or K ) of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives lan explicit order such that the Cl geometrical structure of a function germ is preserved l after higher order perturbations, which generalizes the result on Cl-G triviality of function germs given by M.A.S.Ruas.

Key words: Cl -RV triviality, Cl-KV triviality, A-isolated, controlled vector field

中图分类号: 

  • 58A35