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

Published 14 Jun 2021 in math.DS and math.CV | (2106.07450v6)

Abstract: We prove that a long iteration of rational maps is expanding near boundaries of bounded type Siegel disks. This leads us to extend Petersen's local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case. A new key feature in the proof is that the puzzles are not used.

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