International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 283-288
doi:10.1155/S0161171200003136
Dynamics of a certain sequence of powers.
Roman Sznajder1
and Kanchan Basnyat2
1Department of Mathematics, Bowie State University, Bowie 20715, Maryland, USA
2Department of Computer Science, Bowie State University, Bowie 20715, Maryland, USA
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 𝒞, we achieved it for positive reals. We also discussed some connection to the Euler's functional equation.