Böttcher-type potential for the secant map
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912526960164864 |
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| author | Freeman, Nicholas |
| author_facet | Freeman, Nicholas |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Böttcher-type potential for the secant map Freeman, Nicholas Dynamical Systems 37F80 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. |
| title | Böttcher-type potential for the secant map |
| topic | Dynamical Systems 37F80 |
| url | https://arxiv.org/abs/2508.05847 |