On dynamics of vertices of locally connected polynomial Julia sets
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- by A. Blokh and G. Levin PDF
- Proc. Amer. Math. Soc. 130 (2002), 3219-3230 Request permission
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.References
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Additional Information
- A. Blokh
- Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
- MR Author ID: 196866
- Email: ablokh@math.uab.edu
- G. Levin
- Affiliation: Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
- Email: levin@math.huji.ac.il
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1912999