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Using a nonperturbative weak noise approach we investigate the interferenceof noise and chaos in simple 1D maps. We replace the noise-driven 1D map by anarea-preserving 2D map modelling the Poincare sections of a conserved dynamicalsystem with unbounded energy manifolds. We analyze the properties of the 2D mapand draw conclusions concerning the interference of noise on the nonlinear timeevolution. We apply this technique to the standard period-doubling sequence inthe logistic map. From the 2D area-preserving analogue we, in addition to theusual period-doubling sequence, obtain a series of period doubled cycles whichare elliptic in nature. These cycles are spinning off the real axis atparameters values corresponding to the standard period doubling events.Comment: 22 pages in revtex and 8 figures in ep

Weak Noise Approach to the Logistic Map