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分支问题的有限决定性和万有开折 被引量:5

Finite Determination and Universal Unfoldings of Bifurcation Problems
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摘要 本文给出了分支问题有限决定的一些充分必要条件,并用横切性条件刻划了分支问题的万有开折。 Some sufficient and necessary conditions for a bifurcation problem to be finite determined are given. Transversality condition is used to characterize the universal unfoldings of bifurcation problems. The equivalence of the infinitesimally stability and the universality of bifurcation problems is proved.
作者 邹建成
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 1998年第4期817-822,共6页 Acta Mathematica Sinica:Chinese Series
基金 国家自然科学基金 北方工业大学科研基金
关键词 有限决定 万有开折 分支问题 finite determination, universal unfolding,bifurcation problem
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同被引文献26

  • 1崔登兰,李养成.等变奇点理论中的─类有限生成模[J].晓庄学院自然科学学报,1996,19(4):11-14. 被引量:10
  • 2[1]Golubitsky,M.,Stewart,I.,Schaeffer,D.G.Singularities and Groups in Bifurcation Theory,Vol 2[M].New York:Springer-Verlag 1988.
  • 3[4]Futer,J.E.,Sitta,A.M.,Stewart,I.Singularity Theory and Equivariant Bifurcation Problems with Parameter Symmetry[J].Math Proc.of the Cambridge Philo.Soc.,1996,120(3).547-578.
  • 4[6]Martinent,T.Singularities of Smooth Functions and Maps[M].London Math.Soc.,Lect,Notes Ser.58,Cambridge University Press,1982.
  • 5[7]Gaffney,T.New Methods in The Classification Theory of Bifurcation Problems[J].Contemporary Mathematics 1986(56):97-116.
  • 6[9]Gervais,J.J.Stability of unfolding in the context of equivarint contact-equivalence[J]. Pacfic J.of Math., 1998,12(2):56-78.
  • 7[1]Golubitsky, M.,Stewart,I.,Schaeffer,D.G.Singularities and Groups in Bifurcation Theory, Vol 2[M]. New York: Springer-Verlag, 1988.
  • 8[4]Futer,J.E.,Sitta,A.M.,Stewart,I. Singularity Theory and Equivariant Bifurcation Problems with Parameter Symmetry[J]. Math Proc. of the Cambridge Philo. Soc.,1996,120(3):547-578.
  • 9[5]Gao shouping,Li yangcheng. The Unfolding of Equivariant Bifurcation Problems with Parameters Symmetry[J]. Acta Math. Scinita. 2004,24B(4):1-9.
  • 10[6]Martinent,T. Singularities of Smooth Functions and Maps[M]. London Math. Soc., Lect. Notes Ser. 58, Cambridge University Press ,1982.

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