On the stable Conley index in Hilbert spaces

Tirasan Khandhawit

doi:10.1007/s11784-015-0252-1

On the stable Conley index in Hilbert spaces

Tirasan Khandhawit

University of Tokyo

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	753-773
Number of pages	21
Journal	Journal of Fixed Point Theory and Applications
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/s11784-015-0252-1
Publication status	Published - 1 Dec 2015
Externally published	Yes

Keywords

Conley index
Conley index in Hilbert spaces
finite-dimensional approximation

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10.1007/s11784-015-0252-1

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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 G{\c e}ba, 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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AB - 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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KW - finite-dimensional approximation

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On the stable Conley index in Hilbert spaces

Abstract

Keywords

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