A proof of the C 1 stability conjecture
Mañé, Ricardo
Publications Mathématiques de l'IHÉS, Tome 66 (1987), p. 161-210 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{PMIHES_1987__66__161_0,
     author = {Ma\~n\'e, Ricardo},
     title = {A proof of the $C^1$ stability conjecture},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {66},
     year = {1987},
     pages = {161-210},
     mrnumber = {89e:58090},
     zbl = {0678.58022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1987__66__161_0}
}

Mañé, Ricardo. A proof of the $C^1$ stability conjecture. Publications Mathématiques de l'IHÉS, Tome 66 (1987) pp. 161-210. http://gdmltest.u-ga.fr/item/PMIHES_1987__66__161_0/

[1] A. Andronov, L. Pontrjagin, Systèmes grossiers, Dokl. Akad. Nauk. SSSR, 14 (1937), 247-251. | JFM 63.0728.01 | Zbl 0016.11301

[2] D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., 90 (1967), 1-235. | MR 36 #7157 | Zbl 0176.19101

[3] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Springer Lecture Notes in Math., 470 (1975). | MR 56 #1364 | Zbl 0308.28010

[4] J. Franks, Necessary conditions for stability of diffeomorphisms, Trans. A.M.S., 158 (1971), 301-308. | MR 44 #1042 | Zbl 0219.58005

[5] J. Guckenheimer, A strange, strange attractor, in The Hopf bifurcation and its applications, Applied Mathematics Series, 19 (1976), 165-178, Springer Verlag. | MR 58 #13209

[6] M. Hirsch, C. Pugh, M. Shub, Invariant manifolds, Springer Lecture Notes in Math., 583 (1977). | MR 58 #18595 | Zbl 0355.58009

[7] R. Labarca, M. J. Pacifico, Stability of singular horseshoes, Topology, 25 (1986), 337-352. | MR 87h:58106 | Zbl 0611.58033

[8] S. T. Liao, On the stability conjecture, Chinese Ann. Math., 1 (1980), 9-30. | MR 82c:58031 | Zbl 0449.58013

[9] R. Mañé, Persistent manifolds are normally hyperbolic, Trans. A.M.S., 246 (1978), 261-283. | MR 80c:58019 | Zbl 0362.58014

[10] R. Mañé, Expansive diffeomorphisms, in Dynamical Systems-Warwick 1974, Springer Lecture Notes in Math., 468 (1975), 162-174. | MR 58 #31263 | Zbl 0309.58016

[11] R. Mañé, Characterization of AS diffeomorphisms, Proc. ELAM III, Springer Lecture Notes in Math., 597 (1977), 389-394. | MR 56 #16695 | Zbl 0359.58011

[12] R. Mañé, An ergodic closing lemma, Ann. of Math., 116 (1982), 503-540. | MR 84f:58070 | Zbl 0511.58029

[13] R. Mañé, On the creation of homoclinic points, Publ. Math. I.H.E.S., 66 (1987), 139-159. | Numdam | MR 89e:58089 | Zbl 0669.58024

[14] S. Newhouse, Lectures on dynamical systems, Progr. in Math., 8 (1980), 1-114. | MR 81m:58028 | Zbl 0444.58001

[15] J. Palis, A note on Ω-stability, in Global Analysis, Proc. Sympos. Pure Math., A.M.S., 14 (1970), 221-222. | MR 42 #5276 | Zbl 0214.50801

[16] J. Palis, S. Smale, Structural stability theorems, in Global Analysis, Proc. Sympos. Pure Math., A.M.S., 14 (1970), 223-231. | MR 42 #2505 | Zbl 0214.50702

[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. | MR 46 #921 | Zbl 0286.34088

[18] V. A. Pliss, On a conjecture due to Smale, Diff. Uravnenija, 8 (1972), 268-282. | MR 45 #8957 | Zbl 0243.34077

[19] C. Pugh, The closing lemma, Amer. J. Math., 89 (1967), 956-1009. | MR 37 #2256 | Zbl 0167.21803

[20] J. Robbin, A structural stability theorem, Ann. of Math., 94 (1971), 447-493. | MR 44 #4783 | Zbl 0224.58005

[21] C. Robinson, Cr structural stability implies Kupka-Smale, in Dynamical Systems, Salvador, 1971, Academic Press 1973, 443-449. | MR 48 #12601 | Zbl 0275.58014

[22] C. Robinson, Structural stability of C1 diffeomorphisms, J. Diff. Eq., 22 (1976), 28-73. | MR 57 #14051 | Zbl 0343.58009

[23] M. Shub, Stabilité globale des systèmes dynamiques, Astérisque, 56 (1978). | MR 80c:58015 | Zbl 0396.58014

[24] S. Smale, Diffeomorphisms with many periodic points, in Differential and Combinatorial Topology, Princeton Univ. Press, 1964, 63-80. | MR 31 #6244 | Zbl 0142.41103

[25] S. Smale, Differentiable dynamical systems, Bull. A.M.S., 73 (1967), 747-817. | MR 37 #3598 | Zbl 0202.55202

[26] S. Smale, The Ω-stability theorem, in Global Analysis, Proc. Sympos. Pure Math., A.M.S., 14 (1970), 289-297. | MR 42 #6852 | Zbl 0205.54104