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

##### Doc. Math. 24, 163-173 (2019)
DOI: 10.25537/dm.2019v24.163-173

### Summary

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.

### Mathematics Subject Classification

37F10, 37F50, 30D05, 32H50

### Keywords/Phrases

polynomial diffeomorphisms of $\mathbb{C}^2$, Julia set

### References

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### Affiliation

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