MG11 
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Dynamics and particle production in preheating

We study the simple model for the first stage of preheating where a massive inflaton field $\phi$ is coupled to another scalar field $\chi$ with interaction term $g^2\phi^2\chi^2$. We give a full description of the dynamics of the $\chi$ field modes, including the behaviour of the phase, in terms of the iteration of a simple family of circle maps. The parameters of this family of maps are a function of time when the expansion of the universe is taken into account. We show also how to extend this analysis to other preheating models, namely, adding to the initial model a self-interacting term in the inflaton potential.