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Abstract
In this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain the E-cohomological Conley index. We formulate a continuation principle for the E-cohomological Conley index and show that all LS-flows can be continued to LS-gradient flows. We show that the Morse homology of LS-gradient flows computes the E-cohomological Conley index. We use Lyapunov functions to define the Morse–Conley–Floer cohomology in this context, and show that it is also isomorphic to the E-cohomological Conley index.
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Authors (5)
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Thomas O. Rot
- Universität zu Köln
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Robert C.A.M. Vandervorst
- Vrije Universiteit Amsterdam
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
JOURNAL OF DIFFERENTIAL EQUATIONS
no. 263,
edition 11,
pages 7162 - 7186,
ISSN: 0022-0396 - Language:
- English
- Publication year:
- 2017
- Bibliographic description:
- Izydorek M., Rot T., Starostka M., Styborski M., Vandervorst R.: Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces// JOURNAL OF DIFFERENTIAL EQUATIONS. -Vol. 263, iss. 11 (2017), s.7162-7186
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.jde.2017.08.007
- Verified by:
- Gdańsk University of Technology
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