Structural stability and hyperbolic attractors
Author:
Artur Oscar Lopes
Journal:
Trans. Amer. Math. Soc. 252 (1979), 205219
MSC:
Primary 58F10; Secondary 34D30, 58F12
MathSciNet review:
534118
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Abstract 
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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.
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 [1]
 M. Hirsch and C. Pugh, Stable manifolds and hyperbolic sets, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R. I., 1970, pp. 133164. MR 0271991 (42:6872)
 [2]
 J. Palis and S. Smale, Structural stability theorems, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R. I., 1970, pp. 223231. MR 0267603 (42:2505)
 [3]
 R. Mañé, Expansive diffeomorphisms, Dynamical Systems, Lecture Notes in Math., vol. 468, SpringerVerlag, Berlin and New York, 1975, pp. 162174. MR 0650658 (58:31263)
 [4]
 , Contributions to the stability conjecture, Topology (to appear). MR 516217 (84b:58061)
 [5]
 V. A. Pliss, A hypothesis due to Smale, Differential Equations 8 (1972), 203214.
 [6]
 , The location of separatrices of periodic saddlepoint motion of second order differential equations, Differential Equations 7 (1971), 906927.
 [7]
 C. Pugh, The closing lemma, Amer. J. Math. 85 (1967), 9561009. MR 0226669 (37:2256)
 [8]
 J. Robbin, A structural stability theorem, Ann. of Math. 94 (1971), 447493. MR 0287580 (44:4783)
 [9]
 C. Robinson, Structural stability of flows, Lecture Notes in Math., vol. 468, SpringerVerlag, Berlin and New York, 1975, pp. 262277. MR 0650640 (58:31251)
 [10]
 , Structural stability of diffeomorphisms, J. Differential Equations 22 (1976), 2873.
 [11]
 S. Smale, Differential dynamical systems, Bull. Amer. Math. Soc. 73 (1976), 747817.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905341183
PII:
S 00029947(1979)05341183
Keywords:
Structural stability,
Axiom A,
hyperbolic set,
attractor,
stable manifold
Article copyright:
© Copyright 1979
American Mathematical Society
