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Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets

Peter Makienko
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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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Peter Makienko. 2005-06-08. Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets. https://arxiv.org/abs/math/0506141

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