International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 4, Pages 283-288

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

Received 14 September 1998; Revised 15 January 1999

Copyright © 2000 Roman Sznajder and Kanchan Basnyat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For any nonzero complex number z we define a sequence a1(z)=z, a2(z)=za1(z),,an+1(z)=zan(z), 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.