A characterization of postcritically minimal Newton maps of complex exponential functions

Abstract

We obtain a unique, canonical one-to-one correspondence between the space of marked postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of entire maps that take the form $p(z)\text{exp}(q(z))$ for $p(z)$, $q(z)$ polynomials and $\text{exp}(z)$, the complex exponential function. This bijection preserves the dynamics and embedding of Julia sets and is induced by a surgery tool developed by Haïssinsky.

Final version with changed title

References in corpus (4)

• Newton's method in practice: finding all roots of polynomials of degree one million efficiently
• Accesses to infinity from Fatou components
• Newton maps of complex exponential functions and parabolic surgery
• Hyperbolic-parabolic deformations of rational maps

Cited by in corpus (1)

• Dynamics on immediate basins for parabolic Newton maps