Strong shift equivalence and strong Conley index

ABSTRACT

Using the strong shift equivalence of pointed space maps associated to filtration pairs for isolated invariant sets of a discrete dynamical system we define a strong Conley index independent of the choice of filtration pairs and prove that it is invariant under continuation.

KEYWORDS:

• Elementary strong shift equivalence
• strong shift equivalence
• the Conley index and strong Conley index
• continuation

MCS/CCS/AMS Classification/CR Category numbers:

• 55N10
• 55Q05
• 37D99
• 37B30
• 37B10

Acknowledgements

The authors would like to thank the referee for a very careful reading of the manuscript and for making a number of valuable suggestions, including a suggestion to make some arguments neater.

Disclosure statement

No potential conflict of interest was reported by the authors.