The Julia sets of basic uniCremer polynomials of arbitrary degree

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

2008-09-05

arxiv.org/abs/0809.1071v1

Conformal Geometry and Dynamics , 13 (2009), 139-159

Mathematics

Dynamical Systems

27 pages; 1 figure

Scientific paper

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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