# Dynamic rays of bounded-type entire functions

## Bibliographic data

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