Bursts in average lifetime of transients for chaotic logistic map with a hole (original) (raw)

Chaotic transients are studied for a logistic map at rϭ4, with an inserted narrow hole. We find that average lifetime of chaotic transients that are dependent on the hole position roughly follows the Frobenius-Perron semicircle pattern in most of the unit interval, but at the positions that correspond to the low period ͑1,2,3,. . .), unstable periodic orbits of the logistic map at rϭ4 there are bursts of. An asymptotic relation between the Frobenius-Perron and Kantz-Grassberger average lifetimes, at these positions, is obtained and explained in terms of missing preimages determined from a transient time map. The addition of noise leads to the destruction of bursts of average lifetime. ͓S1063-651X͑97͒11204-1͔