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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |