  We consider preheating in models in which the potential for the inflaton is
given by a fractional power, as is the case in axion monodromy inflation. We
assume a standard coupling between the inflaton field and a scalar matter
field. We find that in spite of the fact that the oscillation of the inflaton
about the field value which minimizes the potential is anharmonic, there is
nevertheless a parametric resonance instability, and we determine the Floquet
exponent which describes this instability as a function of the parameters of
the inflaton potential.
