On infinite area for complex exponential function (Q1766579)

This article discusses (relaxed) Newton's method as applied to the two functions \(z\exp(z)\) and \(z\exp(z^2)\). The result is that the attracting basin of the root \(z=0\) has infinite area in both cases. The paper contains many computer pictures of the attracting domains, unfortunately labelled as ``red'' and ``purple'' but printed in grey; the colored versions can be found online. Here are some updates on the cited references: \textit{D. S. Alexander}'s thesis of 1992 cited as [1] has appeared in 1994 in book form ``A history of complex dynamics. From Schröder to Fatou and Julia (1994; Zbl 0788.30001), and Sutherland's 1990 preprint cited as [13] has appeared in 2001 [\textit{J. Hubbard}, the reviewer and \textit{S. Sutherland}, Invent. Math. 146, No. 1, 1--33 (2001; Zbl 1048.37046)].