Julia sets and bifurcation loci
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910713063145472 |
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| author | Gauthier, Thomas Vigny, Gabriel |
| author_facet | Gauthier, Thomas Vigny, Gabriel |
| contents | We prove that several dynamically defined fractals in $\mathbb{C}$ and $\mathbb{C}^2$ which arise from different type of polynomial dynamical systems can not be the same objects. One of our main results is that the closure of Misiurewicz PCF cubic polynomials (the strong bifurcation locus) cannot be the Julia set of a regular polynomial endomorphism of $\mathbb{C}^2$. We also show that the Julia set of a Hénon map and a polynomial endomorphism cannot coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Julia sets and bifurcation loci Gauthier, Thomas Vigny, Gabriel Dynamical Systems Complex Variables 37F10, 37P30, 37F46 We prove that several dynamically defined fractals in $\mathbb{C}$ and $\mathbb{C}^2$ which arise from different type of polynomial dynamical systems can not be the same objects. One of our main results is that the closure of Misiurewicz PCF cubic polynomials (the strong bifurcation locus) cannot be the Julia set of a regular polynomial endomorphism of $\mathbb{C}^2$. We also show that the Julia set of a Hénon map and a polynomial endomorphism cannot coincide. |
| title | Julia sets and bifurcation loci |
| topic | Dynamical Systems Complex Variables 37F10, 37P30, 37F46 |
| url | https://arxiv.org/abs/2411.16178 |