## The Julia sets of basic uniCremer polynomials of arbitrary degree

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- by Alexander Blokh and Lex Oversteegen
- Conform. Geom. Dyn.
**13**(2009), 139-159 - DOI: https://doi.org/10.1090/S1088-4173-09-00195-7
- Published electronically: June 17, 2009
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## Abstract:

Let $P$ be a polynomial of degree $d$ with a Cremer point $p$ and no repelling or parabolic periodic bi-accessible points. We show that there are two types of such Julia sets $J_P$. The*red dwarf*$J_P$ are nowhere connected im kleinen and such that the intersection of all impressions of external angles is a continuum containing $p$ and the orbits of all critical images. The

*solar*$J_P$ are such that every angle with dense orbit has a degenerate impression disjoint from other impressions and $J_P$ is connected im kleinen at its landing point. We study bi-accessible points and locally connected models of $J_P$ and show that such sets $J_P$ appear through polynomial-like maps for generic polynomials with Cremer points. Since known tools break down for $d>2$ (if $d>2$, it is not known if there are

*small cycles*near $p$, while if $d=2$, this result is due to Yoccoz), we introduce

*wandering ray continua*in $J_P$ and provide a new application of

*Thurston laminations*.

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## Bibliographic Information

**Alexander Blokh**- Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170
- MR Author ID: 196866
- Email: ablokh@math.uab.edu
**Lex Oversteegen**- Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170
- MR Author ID: 134850
- Email: overstee@math.uab.edu
- Received by editor(s): May 8, 2008
- Published electronically: June 17, 2009
- Additional Notes: The first author was partially supported by NSF grant DMS-0456748

The second author was partially supported by NSF grant DMS-0405774 - © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**13**(2009), 139-159 - MSC (2000): Primary 37F10; Secondary 37F50, 37B45, 37C25, 54F15
- DOI: https://doi.org/10.1090/S1088-4173-09-00195-7
- MathSciNet review: 2511916