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arXiv · 2305.18245

Dynamical approximation of postsingularly finite exponentials

Malavika Mukundan
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Abstract

Given any postsingularly finite exponential function $p_\lambda(z) = \lambda \exp(z)$ where $\lambda \in \C^*$, we construct a sequence of postcritically finite unicritical polynomials $p_{d,\lambda_d}(z) = \lambda_d(1+\frac{z}{d})^d$ that converge to $p_\lambda$ locally uniformly in $\C$, with the same postsingular portrait as that of $p_\lambda$. We describe $\lambda_d$ in terms of parameter rays in the space of degree $d$ unicritical polynomials, and exhibit a relationship between the angles of these parameter rays as $d \rightarrow \infty$ and the external addresses associated with $\lambda$ in the exponential parameter plane.

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Malavika Mukundan. 2023-05-29. Dynamical approximation of postsingularly finite exponentials. https://arxiv.org/abs/2305.18245

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