A proof of the C1 stability conjecture

  • Ricardo Mañé
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References

  1. [1]
    A. Andronov, L. Pontrjagin, Systèmes grossiers,Dokl. Akad. Nauk. SSSR,14 (1937), 247–251.Google Scholar
  2. [2]
    D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature,Proc. Steklov Inst. Math.,90 (1967), 1–235.Google Scholar
  3. [3]
    R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms,Springer Lecture Notes in Math.,470 (1975).Google Scholar
  4. [4]
    J. Franks, Necessary conditions for stability of diffeomorphisms,Trans. A.M.S.,158 (1971), 301–308.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    J. Guckenheimer, A strange, strange attractor, inThe Hopf bifurcation and its applications, Applied Mathematics Series,19 (1976), 165–178, Springer Verlag.MathSciNetGoogle Scholar
  6. [6]
    M. Hirsch, C. Pugh, M. Shub, Invariant manifolds,Springer Lecture Notes in Math.,583 (1977).Google Scholar
  7. [7]
    R. Labarca, M. J. Pacifico, Stability of singular horseshoes,Topology,25 (1986), 337–352.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    S. T. Liao, On the stability conjecture,Chinese Ann. Math.,1 (1980), 9–30.MATHMathSciNetGoogle Scholar
  9. [9]
    R. Mañé, Persistent manifolds are normally hyperbolic,Trans. A.M.S.,246 (1978), 261–283.MATHCrossRefGoogle Scholar
  10. [10]
    R. Mañé, Expansive diffeomorphisms, inDynamical Systems-Warwick 1974,Springer Lecture Notes in Math.,468 (1975), 162–174.Google Scholar
  11. [11]
    R. Mañé, Characterization of AS diffeomorphisms,Proc. ELAM III, Springer Lecture Notes in Math.,597 (1977), 389–394.Google Scholar
  12. [12]
    R. Mañé, An ergodic closing lemma,Ann. of Math.,116 (1982), 503–540.CrossRefMathSciNetGoogle Scholar
  13. [13]
    R. Mañé, On the creation of homoclinic points,Publ. Math. I.H.E.S.,66 (1987), 139–159.Google Scholar
  14. [14]
    S. Newhouse, Lectures on dynamical systems,Progr. in Math.,8 (1980), 1–114.MathSciNetGoogle Scholar
  15. [15]
    J. Palis, A note on Ω-stability, inGlobal Analysis, Proc. Sympos. Pure Math., A.M.S.,14 (1970), 221–222.MathSciNetGoogle Scholar
  16. [16]
    J. Palis, S. Smale, Structural stability theorems, inGlobal Analysis, Proc. Sympos. Pure Math., A.M.S.,14 (1970), 223–231.MathSciNetGoogle Scholar
  17. [17]
    V. A. Pliss, Analysis of the necessity of the conditions of Smale and Robbin for structural stability of periodic systems of differential equations,Diff. Uravnenija,8 (1972), 972–983.MATHMathSciNetGoogle Scholar
  18. [18]
    V. A. Pliss, On a conjecture due to Smale,Diff. Uravnenija,8 (1972), 268–282.MATHMathSciNetGoogle Scholar
  19. [19]
    C. Pugh, The closing lemma,Amer. J. Math.,89 (1967), 956–1009.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    J. Robbin, A structural stability theorem,Ann. of Math.,94 (1971), 447–493.CrossRefMathSciNetGoogle Scholar
  21. [21]
    C. Robinson, Cr structural stability implies Kupka-Smale, inDynamical Systems, Salvador, 1971, Academic Press 1973, 443–449.Google Scholar
  22. [22]
    C. Robinson, Structural stability of C1 diffeomorphisms,J. Diff. Eq.,22 (1976), 28–73.MATHCrossRefGoogle Scholar
  23. [23]
    M. Shub, Stabilité globale des systèmes dynamiques,Astérisque, 56 (1978).Google Scholar
  24. [24]
    S. Smale, Diffeomorphisms with many periodic points, inDifferential and Combinatorial Topology, Princeton Univ. Press, 1964, 63–80.Google Scholar
  25. [25]
    S. Smale, Differentiable dynamical systems,Bull. A.M.S.,73 (1967), 747–817.CrossRefMathSciNetGoogle Scholar
  26. [26]
    S. Smale, The Ω-stability theorem, inGlobal Analysis, Proc. Sympos. Pure Math., A.M.S.,14 (1970), 289–297.MathSciNetGoogle Scholar

Copyright information

© Publications Mathématiques de L’I.É.E.S. 1987

Authors and Affiliations

  • Ricardo Mañé
    • 1
  1. 1.Instituto de Matemática Pura e Aplicada (IMPA)Rio de Janeiro - RJ

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