Structural stability and hyperbolic attractors
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- by Artur Oscar Lopes PDF
- Trans. Amer. Math. Soc. 252 (1979), 205-219 Request permission
Abstract:
A necessary condition for structural stability is presented that in the two dimensional case means that the system has a finite number of topological attractors.References
- Morris W. Hirsch and Charles C. Pugh, Stable manifolds and hyperbolic sets, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 133–163. MR 0271991
- J. Palis and S. Smale, Structural stability theorems, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 223–231. MR 0267603
- Ricardo Mañé, Expansive diffeomorphisms, Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), Lecture Notes in Math., Vol. 468, Springer, Berlin, 1975, pp. 162–174. MR 0650658
- Ricardo Mañé, Contributions to the stability conjecture, Topology 17 (1978), no. 4, 383–396. MR 516217, DOI 10.1016/0040-9383(78)90005-8 V. A. Pliss, A hypothesis due to Smale, Differential Equations 8 (1972), 203-214. —, The location of separatrices of periodic saddle-point motion of second order differential equations, Differential Equations 7 (1971), 906-927.
- Charles C. Pugh, The closing lemma, Amer. J. Math. 89 (1967), 956–1009. MR 226669, DOI 10.2307/2373413
- J. W. Robbin, A structural stability theorem, Ann. of Math. (2) 94 (1971), 447–493. MR 287580, DOI 10.2307/1970766
- R. Clark Robinson, Structural stability of $C^{1}$ flows, Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), Lecture Notes in Math., Vol. 468, Springer, Berlin, 1975, pp. 262–277. MR 0650640 —, Structural stability of ${C^1}$ diffeomorphisms, J. Differential Equations 22 (1976), 28-73. S. Smale, Differential dynamical systems, Bull. Amer. Math. Soc. 73 (1976), 747-817.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 252 (1979), 205-219
- MSC: Primary 58F10; Secondary 34D30, 58F12
- DOI: https://doi.org/10.1090/S0002-9947-1979-0534118-3
- MathSciNet review: 534118