Shift Equivalence and the Conley index

Details Shift Equivalence and the Conley index Shift Equivalence and the Conley index

1999-10-29

arxiv.org/abs/math/9910171v1

Mathematics

Dynamical Systems

23 pages

Scientific paper

In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an invariant of the isolated invariant set. Moreover, the maps defining the shift equivalence can be chosen canonically. Lastly, we define partially ordered Morse decompositions and prove the existence of Morse set filtrations for such decompositions.

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