Julia Sets for Polynomial Diffeomorphisms of $\mathbb{C}^2$ are not Semianalytic

Eric Bedford; Kyounghee Kim

doi:10.4171/dm/677

JournalsdmVol. 24pp. 163–173

Julia Sets for Polynomial Diffeomorphisms of $\mathbb{C}^2$ are not Semianalytic

Eric Bedford
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
Kyounghee Kim
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA

$Julia Sets for Polynomial Diffeomorphisms of $\mathbb{C}^2$ are not Semianalytic cover$

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Abstract

For any polynomial diffeomorphism $f$ of $\mathbb{C}^2$ with positive entropy, neither the Julia set of $f$ nor of its inverse $f^{-1}$ is semianalytic.

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Eric Bedford, Kyounghee Kim, Julia Sets for Polynomial Diffeomorphisms of $\mathbb{C}^2$ are not Semianalytic. Doc. Math. 24 (2019), pp. 163–173

DOI 10.4171/DM/677