Izydorek, Marek ORCID: 0000-0003-4219-2197, Rot, Thomas O., Starostka, Maciej, Styborski, Marcin and Vandervorst, Robert C. A. M. (2017). Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces. J. Differ. Equ., 263 (11). S. 7162 - 7187. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2732
Full text not available from this repository.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. (c) 2017 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||||||||||||||||||||||
Creators: |
|
||||||||||||||||||||||||
URN: | urn:nbn:de:hbz:38-208187 | ||||||||||||||||||||||||
DOI: | 10.1016/j.jde.2017.08.007 | ||||||||||||||||||||||||
Journal or Publication Title: | J. Differ. Equ. | ||||||||||||||||||||||||
Volume: | 263 | ||||||||||||||||||||||||
Number: | 11 | ||||||||||||||||||||||||
Page Range: | S. 7162 - 7187 | ||||||||||||||||||||||||
Date: | 2017 | ||||||||||||||||||||||||
Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||||||||||||||||||||||
Place of Publication: | SAN DIEGO | ||||||||||||||||||||||||
ISSN: | 1090-2732 | ||||||||||||||||||||||||
Language: | English | ||||||||||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||||||||||
Subjects: | no entry | ||||||||||||||||||||||||
Uncontrolled Keywords: |
|
||||||||||||||||||||||||
Refereed: | Yes | ||||||||||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/20818 |
Downloads
Downloads per month over past year
Altmetric
Export
Actions (login required)
View Item |