# Julia sets for polynomial diffeomorphisms of ${\Bbb C}^2$ are not semianalytic

## TL;DR

This paper proves that for polynomial diffeomorphisms of complex two-space with positive entropy, their Julia sets and those of their inverses are not semi-analytic, highlighting complex geometric properties.

## Contribution

It establishes that Julia sets for such polynomial diffeomorphisms are not semi-analytic, revealing new geometric constraints in complex dynamics.

## Key findings

- Julia sets are not semi-analytic for positive entropy diffeomorphisms
- Julia sets of the inverse map share the same non-semi-analytic property
- The result applies to all polynomial diffeomorphisms with positive entropy

## Abstract

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