Julia Sets of Certain Exponential Functions

We characterize the Julia sets of certain exponential functions.W e show that the Julia sets J Fλn of Fλn z = λnezn where λn > 0 is the whole plane , provided that limk→∞ Fk λn 0 = ∞.In particular, this is true when λn are real numbers such that λn > 1 ne 1/n.On the other hand, if 0 < λn < 1 ne 1/n, then J Fλn is nowhere dense in and is the complement of the basin of attraction of the unique real attractive fixed point of Fλn.W e then prove similar results for the functions F1 2 n m z = λ1a λ2a···λna λn+1zm n 2 1 where λi ∈ − 0 1 ≤ i ≤ n + 1 aj > 1, 1 ≤ j ≤ n, and m n ≥ 1.