See below in addition for Theses and Books that do not appear on the above lists, as well as a (sporadically maintained) list of errata.

Theses

• Dynamics of Exponential Maps , doctoral thesis, Christian-Albrechts-Universität Kiel, May 2003.
  (Also available on the Dynamical Systems Thesis Server at the SUNY Stony Brook .
• A Limit Problem for Online Scheduling , Rapport de Stage, DEA Algorithmique, Universite de Paris-Sud, 2002.

Books

• With Rebecca Waldecker: Primzahltests für Einsteiger (German); Vieweg+Teubner, 2009. Front matter, back matter and extracts from Sections 1.1 and 2.1.
• With Rebecca Waldecker: Primality testing for beginners (translation/adaptation from the German version). AMS Student Mathematical Library, 2014.

Summaries and errata

Please see below some misprints and errata. These are very old; I was maintaining a list of misprints and errata on a wiki site, but unfortunately this has been deleted so they are lost! If you have further misprints, please let me know.

Topological dynamics of exponential maps on their escaping sets

Ergodic Theory Dynam. Systems 26 (2006), no. 6, 1939 - 1975. arXiv:math.DS/0309107; published version.

Errata:

• In the proof of Theorem 1.1, on page 1950, the number R should be defined as R:=exp(Q(K)+1)+K, instead of R:=Q(K)+1. (Many thanks to Anup Raja Lamichhane for pointing out this error.)

Prime ends and local connectivity

Bull. London Math. Soc. 40 (2008), no. 4, 817 - 826. arxiv:math.GN/0309022. Published version: Abstract, PDF.

Note (March 2012):Donald Sarason has kindly pointed out that Theorem 1.1 was proved by Marie Torhorst in 1918 in her dissertation (Über die Randmenge einfach-zusammenhängender ebener Gebiete); the result was published in Math. Z. in 1921. It appears that this result had largely been forgotten: I could not find a single reference to Torhorst on MathSciNet, and no-one I spoke to about my paper while I was preparing it was aware of it either!

Moreover, Don himself wrote a paper with the exact same title as mine in the 1960s, which reproves Torhorst's result from the work of Ursell and Young, which is the same argument by which Theorem 1.1 is established in my paper. However, his paper was not accepted for publication at the time, as he explains:

I submitted the paper to the Michigan Math. J., then edited by George Piranian, the person who taught me about prime ends and much more about complex analysis. (George is one of my mathematical heroes.) George discussed the paper with Collingwood, one of his collaborators. Their conclusion was that interest in prime ends at the time was at such a low ebb that the paper was likely to be largely ignored.

I did publish an abstract of the paper in the Notices of the A.M.S. (Vol 16 (1969), p. 701). At the time the Notices published abstracts of talks given at society meetings, plus what I think were called by-title abstracts, which any member of the society could use to announce a result. If my memory is correct, I received as a result of the abstract only one request for a copy of the paper.

Don's 1960s manuscript, along with George Piranian's letter and the announcement in the Notices, are contained in this PDF file, which he has kindly allowed me to make available.

To my knowledge, Theorem 1.3, which a characterization of local connectivity at a point and from which Theorem 1.1 follows using the Ursell-Young result, has not previously appeared elsewhere. (Note, however, that the argument that proves the "only if" direction is the same as the one that appears already in Don's paper, which also contains the "if" direction in the special case that every prime end whose impression contains the point in question is of the first kind.)

Please read the arXiv version of the paper, which has been updated with a summary of this, as well as additional historical remarks on Marie Torhorst, and why the famous theorem about continuous extension of Riemann maps should be called the Caratheodory-Torhorst theorem.

Hyperbolic dimension and radial Julia sets of transcendental functions

Proc. Amer. Math. Soc. 137 (2009), 1411-1420. arXiv:0712.4267; published version.

Errata:

• The reference [O] should have listed Adam Epstein and Richard Oudkerk as authors, and should have been denoted by [EO].

Dynamic rays of bounded-type entire functions

With Günter Rottenfußer, Johannes Rückert and Dierk Schleicher.

Ann. of Math. 173 (2011), no. 1, 77-125. arxiv:0704.3213; published version.

Errata:

• In part (c) of the statement of Proposition 5.4, M should be M' (twice).

• In the statement of Lemma 5.7 (Linear head-start is preserved by composition), "F_1 has bounded slope and all F_i satisfy uniform linear head-start conditions" should be replaced by "All F_i have bounded slope and satisfy uniform linear head-start conditions." The second paragraph of the proof should be replaced by the following:

  Let $\alpha$ and $\beta$ be such that $F_i\in {ℬ}_{\log }^n(\alpha ,\beta )$ for all $i$ . For $i=1,\dots ,n$ , let $K_i$ and $M_i\text{'}$ be the constants from Proposition 5.4 (c), applied to $F_i$ . We set $K:={\displaystyle \underset{i}{\max }}{K}_i$ and $M:=\max \{\delta ,{\displaystyle \underset{i}{\max }}{M}_i\text{'}\}$ , where $\delta =\delta (\alpha ,\beta ,K,0)$ is the constant from Lemma 5.2. Now fix $i$ and let $T$ be a tract of $F_i$ . Let $w,z\in T$ such that $\mathrm{Re}w>K\mathrm{Re}z+M$ and such that $F_i\left(z\right)$ and $F_i\left(w\right)$ belong to the same tract of $F_{i+1}$ (where we use the convention that $F_{n+1}=F_1$ ). Then $|w-z|\ge \mathrm{Re}w-\mathrm{Re}z>M\ge \delta$ , and Lemma 5.2 gives that

  $\mathrm{Re}{F}_i\left(w\right)>K\mathrm{Re}{F}_i\left(z\right)+M\text{or}\mathrm{Re}{F}_i\left(z\right)>K\mathrm{Re}{F}_i\left(w\right)+M.$

  ()

  By Proposition 5.4 (c), the first inequality must hold. It follows that $G_a$ satisfies a uniform linear head-start condition with constants $K$ and $M$ .

  (Many thanks to Sebastian Vogel for pointing out this error.)