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Let $P$ be a polynomial of degree $d$ with a Cremer point $p$ and norepelling or parabolic periodic bi-accessible points. We show that there aretwo types of such Julia sets $J_P$. The \emph{red dwarf} $J_P$ are nowhereconnected im kleinen and such that the intersection of all impressions ofexternal angles is a continuum containing $p$ and the orbits of all criticalimages. The \emph{solar} $J_P$ are such that every angle with dense orbit has adegenerate impression disjoint from other impressions and $J_P$ is connected imkleinen at its landing point. We study bi-accessible points and locallyconnected models of $J_P$ and show that such sets $J_P$ appear throughpolynomial-like maps for generic polynomials with Cremer points.

The Julia sets of basic uniCremer polynomials of arbitrary degree