arXiv 0809.10712008-09-05math.DSmath.GT

The Julia sets of basic uniCremer polynomials of arbitrary degree

A. Blokh, L. Oversteegen

备注：: 27 pages; 1 figure
发表信息：: Conformal Geometry and Dynamics, 13 (2009), 139-159

英文摘要：

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 \emph{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 \emph{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.

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