NOISY ONE-DIMENSIONAL MAPS NEAR A CRISIS .2. GENERAL UNCORRELATED WEAK NOISE

The escape rate for one-dimensional noisy maps near a crisis is invest igated. A previously introduced perturbation theory is extended to ver y general kinds of weak uncorrelated noise, including multiplicative w hite noise as a special case. For single-humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law f or the rate is derived. It predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum o f the map is of sufficiently large order. A simple heuristic explanati on of this effect is given. The escape rate is discussed in detail for noise distributions of Levy, dichotomous, and exponential type. In th e latter case, the rate is dominated by an exponentially leading Arrhe nius factor in the deep precritical regime. However, the preexponentia l factor may still depend more strongly than any power law on the nois e strength.