When all asymptotic values of a Nevanlinna function land at infinity, its Julia set is the full sphere and the map acts non-ergodically there.
Ergodic exponential maps with escaping singular behaviours
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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.
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2024 1verdicts
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Meromorphic functions whose action on their Julia sets is Non-Ergodic
When all asymptotic values of a Nevanlinna function land at infinity, its Julia set is the full sphere and the map acts non-ergodically there.