A geometric Morse-Novikov complex with infinite series coefficients

Let M be a closed n-dimensional manifold, n > 2, whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form $\alpha$ on M , closed but non-exact, and a pseudo-gradient X such that the differential $\mathrm{\partial }$ X of the Novikov complex of the pair ($\alpha$, X) has at least one incidence coefficient which is an infinite series. This is an application of our previous study of the homoclinic bifurcation of pseudo-gradients of multivalued Morse functions.