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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003136 |
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| _version_ | 1849404939680350208 |
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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 |
| id | doaj-art-99a473e03a3443ec9f3ba3ce9583a5d7 |
| 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 |