No smooth Julia sets for polynomial diffeomorphisms of $\mathbb{C}^2$ with positive entropy

Eric Bedford; Kyounghee Kim

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arXiv · 1506.01456

No smooth Julia sets for polynomial diffeomorphisms of $\mathbb{C}^2$ with positive entropy

Eric Bedford·Kyounghee Kim

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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 $C^1$ smooth as a manifold-with-boundary.

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BibTeX RIS

Eric Bedford, Kyounghee Kim. 2015-06-04. No smooth Julia sets for polynomial diffeomorphisms of $\mathbb{C}^2$ with positive entropy. https://arxiv.org/abs/1506.01456

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