  We have introduced a new transfer operator for chaotic flows whose leading
eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied
cycle expansion of the Fredholm determinant of the new operator to evaluation
of its spectrum. The theory hs been tested on a normal form model of the vector
advecting dynamical flow. If the model is a simple map with constant time
between two iterations, the dynamo rate is the same as the escape rate of
scalar quantties. However, a spread in Poincar\'e section return times lifts
the degeneracy of the vector and scalar advection rates, and leads to dynamo
rates that dominate over the scalar advection rates. For sufficiently large
time spreads we have even found repellers for which the magnetic field grows
exponentially, even though the scalar densities are decaying exponentially.
