Dynamics of a certain sequence of powers

Roman Sznajder and Kanchan Basnyat

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-6

Abstract:

For any nonzero complex number z we define a sequence a 1 ( z ) = z , a 2 ( z ) = z a 1 ( z ) , … , a n + 1 ( z ) = z a n ( z ) , n ∈ ℕ . We attempt to describe the set of these z for which the sequence { a n ( 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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:564708

DOI: 10.1155/S0161171200003136

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