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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.05847 |
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Table of Contents:
- We present a construction of a Böttcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the Böttcher-type map extends to be continuous on the entire basin of attraction of the fixed point, and is real-analytic away from the iterated preimages of the fixed point. Using this construction, we show the associated Green's function for the fixed point is pluriharmonic wherever it is finite.