  We study the consequences of noise and dissipation for parametric resonance
during preheating. The effective equations of motion for the inflaton and the
radiation field are obtained and shown to present self-consistent noise and
dissipation terms. The equations exhibit the usual parametric resonance
phenomenon, allowing for exponential amplification of the radiation modes
inside the instability bands. By focusing on the dimension of the border of
those bands we explicitly show that they are fractal, indicating the strong
dependence of the outcome in the initial conditions. The simultaneous effect of
noise and dissipation to the fractality of the borders are then examined.
