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On dynamics of vertices of locally connected polynomial Julia sets


Authors: A. Blokh and G. Levin
Journal: Proc. Amer. Math. Soc. 130 (2002), 3219-3230
MSC (2000): Primary 37F10; Secondary 37E25
DOI: https://doi.org/10.1090/S0002-9939-02-06698-4
Published electronically: May 29, 2002
MathSciNet review: 1912999
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $P$ be a polynomial whose Julia set $J$ is locally connected. Then a non-preperiodic non-precritical vertex of $J$must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of $P$. In particular, if all critical points of $P$ are non-recurrent then all vertices of $J$ are preperiodic or precritical.


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Additional Information

A. Blokh
Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
Email: ablokh@math.uab.edu

G. Levin
Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
Email: levin@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9939-02-06698-4
Keywords: Julia set, vertices, laminations, recurrent critical points
Received by editor(s): December 22, 2000
Published electronically: May 29, 2002
Additional Notes: The first author was partially supported by NSF grant DMS 9970363.
Communicated by: Michael Handel
Article copyright: © Copyright 2002 American Mathematical Society