Universität zu Köln

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

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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. (c) 2017 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Izydorek, Marek UNSPECIFIED orcid.org/0000-0003-4219-2197 UNSPECIFIED Rot, Thomas O. UNSPECIFIED UNSPECIFIED UNSPECIFIED Starostka, Maciej UNSPECIFIED UNSPECIFIED UNSPECIFIED Styborski, Marcin UNSPECIFIED UNSPECIFIED UNSPECIFIED Vandervorst, Robert C. A. M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
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:	Keywords Language FLOER HOMOLOGY; SYSTEMS; COMPLEX Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/20818