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Eremenko’s conjecture, wandering Lakes of Wada, and maverick points

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This work demonstrates a counterexample to Eremenko's conjecture in complex dynamics, suggesting new insights into Fatou components.

A counterexample to Eremenko's conjecture shows not all components of escaping points are unbounded.
The existence of Lakes of Wada continua in complex dynamics is confirmed with infinite Fatou components sharing boundaries.
Maverick points on wandering domain boundaries may have positive Lebesgue measure but zero harmonic measure.
An entire function is presented with a simply connected Fatou component and a disconnected complement.

Martí‐Pete et al. (2025) studied this question.

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