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Mathematics  2015 

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

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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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