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A refinement of the Conley index and an application to the stability of hyperbolic invariant sets. (English) Zbl 0633.58040
The author considers a continuous flow on the locally compact Hausdorff space \(\Gamma\). It is known that the compact and isolated invariant set S of this flow possesses a Conley index [C. Conley, Isolated invariant sets and the Morse index (1978; Zbl 0397.34056); C. Conley and E. Zehnder, Physica A 124, 649-657 (1984; Zbl 0605.58015)], which is the homotopy type of a pointed compact space. The author shows that an additional structure can be used to define an additional invariant of S under continuation, which carries along some topology of S itself. In the case when a normally hyperbolic invariant manifold S is a retract of \(\Gamma\), he proves a global and topological continuation-theorem [see also N. Fenichel, Indiana Univ. Math. J. 21, 193-226 (1971; Zbl 0246.58015)].
Reviewer: A.Kanevskij

MSC:
37C10 Dynamics induced by flows and semiflows
37D99 Dynamical systems with hyperbolic behavior
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[1] DOI: 10.1007/BF01390270 · Zbl 0403.57001 · doi:10.1007/BF01390270
[2] DOI: 10.1002/cpa.3160370204 · Zbl 0559.58019 · doi:10.1002/cpa.3160370204
[3] Conley, Isolated Invariant Sets and the Morse Index. 38 pp none– (1978) · Zbl 0397.34056
[4] Hirsch, Invariant Manifolds (1977) · doi:10.1007/BFb0092042
[5] DOI: 10.1512/iumj.1971.21.21017 · Zbl 0246.58015 · doi:10.1512/iumj.1971.21.21017
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