The connection map for attractor-repeller pairs

McCord, Christopher

doi:10.1090/S0002-9947-1988-0936812-4

The connection map for attractor-repeller pairs

Author: Christopher McCord
Journal: Trans. Amer. Math. Soc. 307 (1988), 195-203
MSC: Primary 58F12; Secondary 34C35
DOI: https://doi.org/10.1090/S0002-9947-1988-0936812-4
MathSciNet review: 936812
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Abstract: In the Conley index theory, the connection map of the homology attractor-repeller sequence provides a means of detecting connecting orbits between a repeller and attractor in an isolated invariant set. In this work, the connection map is shown to be additive: under suitable decompositions of the connecting orbit set, the connection map of the invariant set equals the sum of the connection maps of the decomposition elements. This refines the information provided by the homology attractor-repeller sequence. In particular, the properties of the connection map lead to a characterization of isolated invariant sets with hyperbolic critical points as an attractor-repeller pair.

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