B\"ottcher-type potential for the secant map
Dynamical Systems
2025-08-11 v1
Abstract
We present a construction of a B\"ottcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the B\"ottcher-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.
Cite
@article{arxiv.2508.05847,
title = {B\"ottcher-type potential for the secant map},
author = {Nicholas Freeman},
journal= {arXiv preprint arXiv:2508.05847},
year = {2025}
}
Comments
32 pages, 4 figures