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Conley Index Theory and Novikov-Morse Theory
Huijun Fan and Jürgen Jost
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.