On dynamics of vertices of locally connected polynomial Julia sets

Blokh, A.; Levin, G.

doi:10.1090/S0002-9939-02-06698-4

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.

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