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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

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


Author: Peter M. Makienko
Journal: Conform. Geom. Dyn. 10 (2006), 197-202
MSC (2000): Primary 37F45; Secondary 37F30
Published electronically: September 6, 2006
MathSciNet review: 2261048
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Peter M. Makienko
Affiliation: Instituto de Matematicas, Av. Universidad S/N., Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico

DOI: http://dx.doi.org/10.1090/S1088-4173-06-00142-1
PII: S 1088-4173(06)00142-1
Received by editor(s): June 13, 2005
Published electronically: September 6, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.