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

Makienko, Peter

doi:10.1090/S1088-4173-06-00142-1

Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets
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by Peter M. Makienko

Conform. Geom. Dyn. 10 (2006), 197-202

DOI: https://doi.org/10.1090/S1088-4173-06-00142-1

Published electronically: September 6, 2006

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Abstract:

Let $R$ be a rational map with a 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 $R$ cannot be a structurally stable map.

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