  Let $M$ be a closed connected manifold, $f$ be a Morse map from $M$ to a
circle, $v$ be a gradient-like vector field satisfying the transversality
condition. The Novikov construction associates to these data a chain complex
$C_*=C_*(f,v)$. There is a chain homotopy equivalence between $C_*$ and
completed simplicial chain complex of the corresponding infinite cyclic
covering of $M$. The first main result of the paper is the construction of a
functorial chain homotopy equivalence between these two complexes. The second
main result states that the torsion of this chain homotopy equivalence equals
to the Lefschetz zeta function of the gradient flow, if $v$ has only hyperbolic
closed orbits.
