数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1249-1256.doi: 10.1016/S0252-9602(10)60121-X

• 论文 • 上一篇    下一篇

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

刘恒兴, 张敦穆   

  1. School of Mathematics and Statistics, |Wuhan University, Wuhan 430072, China
  • 收稿日期:2007-12-29 修回日期:2008-09-19 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

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

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)

摘要:

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.

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

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

中图分类号: 

  • 58A35