Skip to main content
Log in

Another proof forC 1 stability conjecture for flows

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

TheC 1 structural stability conjecture for flows byC 1 connecting lemma and obstruction sets is proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Markus, L., Structurally stable differential systems,Annals of Math., 1961, 73: 1.

    Article  MathSciNet  Google Scholar 

  2. Liao Shantao, On the stability conjecture,Chinese Ann. Math., 1980, 1:9.

    MATH  MathSciNet  Google Scholar 

  3. Liao Shantao,Qualitative Theory of Differential Dynamicsl Systems, Beijing: Science Press, 1996.

    Google Scholar 

  4. Robinson, C.,C structural stability implies Kupka-Smale, in Dynamical System (ed. Pexioto, M.), 1971, New York: Academic Press, 1973, 443–449.

    Google Scholar 

  5. Robinson, C., Structural stability of C1 flows, inDynamical Systems-Warwick 1974, Lecture Notes in Mathematics (ed. Manning, A.), Vol. 468, University of Warwick. 1973/1974, New York: Springer-Verlag, 1975, 262–277.

    Google Scholar 

  6. Pexioto, M., Structural stability on 2-dimensional manifolds,Topology, 1962, 1: 101.

    Article  MathSciNet  Google Scholar 

  7. Palis, J., Smale, S., Structural stability theorems, inGlobal Analysis, Proc. Sympos. Pure Math. (eds. Chern, S. S., Smale, S.), Vol, 14, University of California, Berkeley, 1968, Providence: Amer. Math. Soc. Rhode Island, 1970, 223–231.

    Google Scholar 

  8. Mané, R., An ergodic closing lemma,Ann. of Math., 1982, 116: 503.

    Article  MathSciNet  Google Scholar 

  9. Mané, R., A proof of the C1 stability conjecture,Publ. Math. IHES, 1988, 66: 161.

    MATH  Google Scholar 

  10. Sannami, A., The stability theorems for discrete dynamical systems on two-dimensional manifolds,Nagoya Math. J., 1983, 90: 1.

    MATH  MathSciNet  Google Scholar 

  11. Hu, S., A proof of C1 stability conjecture for three-dimensional flows,Trans. Amer. Math. Soc., 1994, 342: 753.

    Article  MATH  MathSciNet  Google Scholar 

  12. Liao Shantao, Obstruction sets, minimal rambling sets and their applications, inChinese Mathematics into the 2lst Century, Tianjin (eds. Wu Wen-tsun, Cheng Min-de), 1988, Beijing: Peking University Press, 1991, 1–14.

    Google Scholar 

  13. Liao Shantao, Obstruction sets (I),Acta Math. Sinica (in Chinese), 1980, 23: 411.

    MATH  Google Scholar 

  14. Liao Shantao, Obstruction sets (II),Acta Sciencetiarum Naturalium Universitatis Pekinensis, 1981, 2: 1.

    Google Scholar 

  15. Hayashi, S., Connecting invariant manifolds and the solution of the C1 stability conjecture and Ω-stability conjecture for flows,Annals of Math., 1997, 145: 81.

    Article  MATH  Google Scholar 

  16. Wen, L., On the C1 stability conjecture for flows,J. D. E., 1996, 129: 334.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project supported by the National Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gan, S. Another proof forC 1 stability conjecture for flows. Sci. China Ser. A-Math. 41, 1076–1082 (1998). https://doi.org/10.1007/BF02871842

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02871842

Keywords

Navigation