In this paper, I show that the escaping set of the complex exponential map is a connected subset of the plane. This was surprising (to me at least, but I believe also to others); for example, it was known that the path-connected components of this set were all closed and nowhere dense. At this point, escaping sets in the Eremenko-Lyubich set were often thought of as being disconnected, although following this paper it turned out that many escaping sets in the exponential family at least are in fact connected.

Proposition 2.2, which plays an important role in the proof, is in fact established in the course of Devaney's proof in reference [D]. This should have been acknowledged in the paper. (I am not entirely sure how I managed to miss this at the time.)

## The escaping set of the exponential

## Bibliographic data

Ergodic Theory and Dynamical Systems 30 (2010), 595-599 arxiv:0812.1768; published version.## Description

In this paper, I show that theescaping setof the complex exponential map is a connected subset of the plane. This was surprising (to me at least, but I believe also to others); for example, it was known that thepath-connectedcomponents of this set were all closed and nowhere dense. At this point, escaping sets in the Eremenko-Lyubich set were often thought of as being disconnected, although following this paper it turned out that many escaping sets in the exponential family at least are in fact connected.Proposition 2.2, which plays an important role in the proof, is in fact established in the course of Devaney's proof in reference [D]. This should have been acknowledged in the paper. (I am not entirely sure how I managed to miss this at the time.)