S ep 2 00 0 GRADIENT FLOWS OF CLOSED 1 - FORMS AND THEIR CLOSED ORBITS

In [16, 17], Pajitnov considers the closed orbit structure of generic gradient flows of circle-valued Morse functions. It turns out that the torsion of a chain homotopy equivalence between the Novikov complex and the completed simplicial chain complex of the universal cover detects the eta function of the flow. This eta function counts the closed orbits and reduces to the logarithm of the zeta function after abelianizing. We extend this result to the case of closed 1-forms which are Morse. To relate the torsion to the eta function we use the Dennis trace.