Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1249-1256.doi: 10.1016/S0252-9602(10)60121-X

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V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES

 LIU Heng-Xing, ZHANG Dun-Mu   

  1. School of Mathematics and Statistics, |Wuhan University, Wuhan 430072, China
  • Received:2007-12-29 Revised:2008-09-19 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported by the National Nature Science Foundation of China (10671009, 60534080, 10871149)

Abstract:

In this article, we provide estimates for the degree of V-bilipschitz determinacy of weighted homogeneous function germs defined on
weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.

Key words: V-bilipschitz determinacy, weighted homogeneous polynomial function germs, controlled vector field, weighted homogeneous control functions

CLC Number: 

  • 58A35
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