Conley Index Theory and Novikov-Morse Theory

Huijun Fan and Jürgen Jost

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Submission date: 30. Nov. 2003 (revised version: June 2004)
Pages: 37
published in: Pure and applied mathematics quarterly, 1 (2005) 4, p. 939-971 
DOI number (of the published article): 10.4310/PAMQ.2005.v1.n4.a10
Bibtex
MSC-Numbers: 37B30, 37B35, 57R70
Keywords and phrases: conley index, novikov-morse theory, flow carring a cocycle
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Abstract:
We derive the general novikov-morse inequalities in a Conley type framework for flows carrying a cocycle, therefore generalizing our result in [H. Fan, and J. Jost, Novikov Morse theory for dynamical systems, Calc. Var. 17, 29-73(2002)] derived for integral cocycle. The condition for carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distinguished from general flows carrying a cocycle by boundedness conditions on these integrals.