Flows on vector bundles and hyperbolic sets
Authors:
Dietmar Salamon and Eduard Zehnder
Journal:
Trans. Amer. Math. Soc. 306 (1988), 623649
MSC:
Primary 58F15; Secondary 34C35
MathSciNet review:
933310
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Abstract: This note deals with C. Conley's topological approach to hyperbolic invariant sets for continuous flows. It is based on the notions of isolated invariant sets and Morse decompositions and it leads to the concept of weak hyperbolicity.
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 D. V. Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. 90 (1967). MR 0224110 (36:7157)
 [2]
 D. V. Anosov and J. G. Sinai, Some smooth ergodic systems, Russian Math. Surveys 22 (1967), 107172. MR 0224771 (37:370)
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 C. Conley, Hyperbolic sets and shift automorphisms, Dynamical Systems, Theory and Applications (J. Moser, ed.), Lecture Notes in Physics, vol. 38, Springer, New York, 1975, pp. 539549. MR 0455043 (56:13284)
 [4]
 , Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math., no. 38, Amer. Math. Soc., Providence, R.I., 1976.
 [5]
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 [6]
 A. Floer, A topological persistence theorem for normally hyperbolic manifolds via the Conley index, preprint, RuhrUniversität Bochum, 1985.
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 , A refinement of the Conley index and an application to the stability of hyperbolic invariant sets, Bericht Nr. 42, RuhrUniversität Bochum, 1985.
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 J. Moser, On a theorem of Anosov, J. Differential Equations 5 (1969), 411440. MR 0238357 (38:6633)
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 [11]
 J. F. Selgrade, Isolated invariant sets for flows on vector bundles, Trans. Amer. Math. Soc. 203 (1975), 359390. MR 0368080 (51:4322)
 [12]
 R. C. Churchill, J. Franke and J. F. Selgrade, A geometric criterion for hyperbolicity of flows, Proc. Amer. Math. Soc. 62 (1977), 137143. MR 0428358 (55:1382)
 [13]
 R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), 320358. MR 0501182 (58:18604)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198809333109
PII:
S 00029947(1988)09333109
Article copyright:
© Copyright 1988 American Mathematical Society
