S0161171200003136 © Hindawi Publishing Corp. DYNAMICS OF A CERTAIN SEQUENCE OF POWERS

Abstract. For any nonzero complex number z we define a sequence a1(z) = z, a2(z) = za1(z),...,an+1(z) = zan(z), n ∈ N. We attempt to describe the set of these z for which the sequence {an(z)} is convergent. While it is almost impossible to characterize this convergence set in the complex plane, we achieved it for positive reals. We also discussed some connection to the Euler’s functional equation