On the stable Conley index in Hilbert spaces
In this paper, we study Conley theory of flows on a Hilbert space. Our approach is to apply finite-dimensional approximation which is a slight refinement of the construction developed by Gęba, Izydorek, and Pruszko (1999). For instance, we include subspaces other than invariant subspaces in the construction. As a main result, we define a stable Conley index as an object in the stable homotopy category and show that it does not depend on choices in the construction.
KeywordsConley index in Hilbert spaces Conley index finite-dimensional approximation
Mathematics Subject Classification37B30
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