This proof details the singular nature of wandering Julia components in non-recurrent maps, indicating the structure of periodic components.
We prove that every wandering exposed Julia component of a rational map is to a singleton, provided that each wandering Julia component containing critical points is non-recurrent. Moreover, we show that the Julia set contains only finitely many periodic complex-type components if each wandering Julia component containing critical values is non-recurrent.
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Gao et al. (2025) studied this question.
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