Exact packing dimension in random recursive constructions

We explore the exact packing dimension of certain random recursive constructions. In case of polynomial decay at 0 of the distribution function of random variable X, associated with the construction, we prove that it does not exist, and in case of exponential decay it is t|log|logt||, where is the fractal dimension of the limit set and 1/ is the rate of exponential decay.Research supported by the Department of Mathematics and Statistics (Mathematics) at University of Jyväskylä.Mathematics Subject Classification (2000):Primary 28A78, 28A80; Secondary 60D05, 60J80