Local Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries

Abstract

Consider a polynomial $f$ of degree $d\ge 2$ that has a Siegel disk ${\Delta }_f$ with a rotation number of bounded type. We prove that there does not exist a hedgehog containing ${\Delta }_f$. Moreover, if the Julia set $J_f$ of $f$ is connected, then it is locally connected at the Siegel boundary $\partial {\Delta }_f$.

51 pages, 4 figures

References in corpus (1)

• Local connectivity of Julia sets of some rational maps with Siegel disks

Cited by in corpus (1)

• Local connectivity of Julia sets of some rational maps with Siegel disks