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

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.

References in corpus (2)

• Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
• A structure theorem for semi-parabolic Hénon maps