Applied Mathematics and Mechanics

, Volume 5, Issue 6, pp 1745–1750 | Cite as

On characterizations of structural stability

  • Liao Shan-tao


This note takes a sketch of a proof of a characterization theorem for diffeomorphism on a compact 3-dimensional smooth manifold to be structurally stable.


Mathematical Modeling Manifold Industrial Mathematic Structural Stability Smooth Manifold 
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  1. (1).
    Palis, J. and S. Smale, Structural Stability theorems, Global Analysis, Proc. Sympos. Pure Math., Vol. 14, Amer. Math. Soc., Providence, R. I., (1970), 223–231.Google Scholar
  2. (2).
    Robbin, J., A structural stability theorem, Ann. of Math., 94(1971), 447–493.Google Scholar
  3. (3).
    Robinson, C., Structural stability of diffeomorphisms, J. Diff. Equations, 22(1976), 28–73.CrossRefGoogle Scholar
  4. (4).
    Liao Shan-tao, On the stability conjecture, Chinese Annals of Math, 1(1980), 9–29.Google Scholar
  5. (5).
    Mãné, R., An ergodic closing lemma, Annals of Math., 116 (1982), 503–540.Google Scholar
  6. (6).
    Sannami, A., The stability theorems for discrete dynamical systems on two-dimensional manifolds, Nagoya Math, J. 90(1983) (Announcement and Summary: Proc. Japan Acad Ser. A Math. Sci. 57(1981), 403–407.Google Scholar
  7. (7).
    Abraham, R. and J. Robbin, Transversal mappings and flows, Benjamin, New York, 1967.Google Scholar
  8. (8).
    Liao Shan-tao, Obstruction sets and strong transversality, Acta Math. Sinica, 19(1976), 203–209. (in Chinese)Google Scholar
  9. (9).
    Liao Shan-tao, Obstruction sets (I), Acta Math. Sinica, 23(1980), 411–453. (in Chinese)Google Scholar
  10. (10).
    Liao Shao-tao, Obstruction sets (II), Acta Scientiarum Naturalium Universitatis Pekinensis, 1981 No. 2, 1–36. (in Chinese)Google Scholar
  11. (11).
    Liao Shao-tao, A basic property of a certain class of differential systems, Acta Math. Sinica, 22(1979), 316–343. (in Chinese)Google Scholar
  12. (12).
    Liao Shao-tao, An existence theorem for periodic orbits, Acta Scientiarum Naturalium Universitatis Pekinensis, 1979, No. 1, 1–20. (in Chinese)Google Scholar
  13. (13).
    Robinson, C., Structural stability for flows, Lecture Notes, 468, Warwick (1974), Springer-Verlag.Google Scholar
  14. (14).
    Peixoto, M., Structural stability on two dimensional manifolds, Topology, 1(1962), 101–120.CrossRefGoogle Scholar

Copyright information

© HUST Press 1984

Authors and Affiliations

  • Liao Shan-tao
    • 1
  1. 1.Mathematics Department and Mathematics InstitutePeking UniversityBeijing

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