  Using a nonperturbative weak noise approach we investigate the interference
of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an
area-preserving 2D map modelling the Poincare sections of a conserved dynamical
system with unbounded energy manifolds. We analyze the properties of the 2D map
and draw conclusions concerning the interference of noise on the nonlinear time
evolution. We apply this technique to the standard period-doubling sequence in
the logistic map. From the 2D area-preserving analogue we, in addition to the
usual period-doubling sequence, obtain a series of period doubled cycles which
are elliptic in nature. These cycles are spinning off the real axis at
parameters values corresponding to the standard period doubling events.
