Dynamics of a certain sequence of powers

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 pos...

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Main Authors: Roman Sznajder, Kanchan Basnyat
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171200003136
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author Roman Sznajder
Kanchan Basnyat
author_facet Roman Sznajder
Kanchan Basnyat
author_sort Roman Sznajder
collection DOAJ
description 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.
format Article
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institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 2000-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-99a473e03a3443ec9f3ba3ce9583a5d72025-08-20T03:36:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124428328810.1155/S0161171200003136Dynamics of a certain sequence of powersRoman Sznajder0Kanchan Basnyat1Department of Mathematics, Bowie State University, Bowie, Maryland 20715, USADepartment of Computer Science, Bowie State University, Bowie, Maryland 20715, USAFor 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.http://dx.doi.org/10.1155/S0161171200003136Power sequencedynamicsconvergence.
spellingShingle Roman Sznajder
Kanchan Basnyat
Dynamics of a certain sequence of powers
International Journal of Mathematics and Mathematical Sciences
Power sequence
dynamics
convergence.
title Dynamics of a certain sequence of powers
title_full Dynamics of a certain sequence of powers
title_fullStr Dynamics of a certain sequence of powers
title_full_unstemmed Dynamics of a certain sequence of powers
title_short Dynamics of a certain sequence of powers
title_sort dynamics of a certain sequence of powers
topic Power sequence
dynamics
convergence.
url http://dx.doi.org/10.1155/S0161171200003136
work_keys_str_mv AT romansznajder dynamicsofacertainsequenceofpowers
AT kanchanbasnyat dynamicsofacertainsequenceofpowers