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On the stable Conley index in Hilbert spaces

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Abstract

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.

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  1. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, 5-1-5 Kashiwa-No-Ha, Kashiwa, Chiba, 277-8583, Japan

    Tirasan Khandhawit

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  1. Tirasan Khandhawit
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Correspondence to Tirasan Khandhawit.

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Khandhawit, T. On the stable Conley index in Hilbert spaces. J. Fixed Point Theory Appl. 17, 753–773 (2015). https://doi.org/10.1007/s11784-015-0252-1

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