Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets
classification
🧮 math.DS
keywords
disconnectedjulianon-persistentlyrationalrecurrenttotallyconicalcontains
read the original abstract
Let $ R $ be a rational map with totally disconnected Julia set $ J(R). $ If the postcritical set on $ J(R) $ contains a non-persistently recurrent (or conical) point, then we show that the map $ R $ can not be a structurally stable map.
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