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Science in China Series A: Mathematics

, Volume 40, Issue 10, pp 1036–1044 | Cite as

Rigidity result on conjugacies of families of diffeomorphisms

  • Weigu Li
  • Meirong Zhang
Science in China (series A)
  • 16 Downloads

Abstract

Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms, i.e. families of Cr(2⩽r⩽∞) diffeomorphisms, the strongly topologically conjugating homeomorphisms near degenerate saddle-nodes will be differentiable on center manifolds of the saddle-nodes.

Keywords

diffeomorphism topological conjugacy 

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References

  1. 1.
    Liao, S., On the stability conjecture,Chinese Ann. Math., 1980, 1:9.MATHMathSciNetGoogle Scholar
  2. 2.
    Liao, S.,Qualitative Theory of Differentiable Dynamical Systems (in Chinese), Beijing: Science Press, 1996.Google Scholar
  3. 3.
    Manù. R., A proof of the C1 stability conjecture,Puhl. Math. I.H.E.S., 1988, 66:161.Google Scholar
  4. 4.
    Wen, L., On the C1 stability conjecture for flows,J. Differential Equations, 1996, 129:334.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Newhouse, S., Palis, J., Takens, F., Bifurcations and stability of families of diffeomorphisms,Puhl. Math. I.H.E.S., 1983, 53:5.MathSciNetGoogle Scholar
  6. 6.
    Malta, I. R., Palis, J., Families of vector fields with finite modulus of stability,Lecture Notes in Math., Vol. 898, New York-Berlin: Springer-Verlag, 1981, 212–229.Google Scholar
  7. 7.
    Arnold, V.I.,Dynamical Systems V, New York-Berlin: Springer-Verlag, 1991.Google Scholar
  8. 8.
    Li, W., Zhang, Z., Bifurcation systems on surfaces,Nankai Inst. Math. (in Chinese), 1991.Google Scholar
  9. 9.
    Takens, F., Normal forms of certain singularities of vector fields,Ann. Inst. Fourier, 1973, 23(2): 163.MATHMathSciNetGoogle Scholar
  10. 10.
    Beyer, W. A., Channell, P. J., A functional equation for the embedding of a homeomorphism of the interval into a flow,Lecture Notes in Math., Vol. 1163, Berlin: Springer-Verlag, 1985, 1163:7.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhang, M., Embedding problem and functional equations,Acta Math. Sinica, New Ser., 1992, 8:148.MATHCrossRefGoogle Scholar
  12. 12.
    Zhang, M., Li, W., Embedding flows and smooth conjugacy,Chinese Ann. Math., Ser. B, 1997, 18:1.MathSciNetGoogle Scholar
  13. 13.
    Pugh,C. C., Against the C2 closing lemma,J. Differential Equations, 1975, 17:435.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Lam, P.-F. Embedding a differential homeomorphism in a flow,J. Differential Equations, 1978, 30:31.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Firmo, S., Real contractions and C1 conjugations,J. Differential Equations, 1988, 74:1.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science in China Press 1997

Authors and Affiliations

  • Weigu Li
    • 1
  • Meirong Zhang
    • 2
  1. 1.Department of MathematicsPeking UniversityBeijingChina
  2. 2.Department of Applied MathematicsTsinghua UniversityBeijingChina

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