Ergodic exponential maps with escaping singular behaviours

Abstract

We construct exponential maps for which the singular value tends to infinity under iterates while the maps are ergodic. This is in contrast with a result of Lyubich from 1987 which tells that $e^z$ is not ergodic.

9 pages, 1 figure; Theorem 1.2 rephrased and the proof of the main Theorem 1 is reorganized. Author accepted version. To appear in Bulletin of the London Mathematical Society