  We study the model of a massive inflaton field $\phi$ coupled to another
scalar filed $\chi$ with interaction term $g^2\phi^2\chi^2$ for the first stage
of preheating. We obtain the the behavior of the phase in terms of the
iteration of a simple family of circle maps. When expansion of the universe is
taken into account the qualitative behavior of the phase and growth number
evolution is reminiscent of the behavior found in the case without expansion.
