The wandering domain problem for attracting polynomial skew products
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914049867907072 |
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| author | Ji, Zhuchao Shen, Weixiao |
| author_facet | Ji, Zhuchao Shen, Weixiao |
| contents | Wandering Fatou components were recently constructed by Astorg et al for higher-dimensional holomorphic maps on projective spaces. Their examples are polynomial skew products with a parabolic invariant line. In this paper, we study this wandering domain problem for polynomial skew product $f$ with an attracting invariant line $L$ (which is the more common case). We show that if $f$ is unicritical (in the sense that the critical curve has a unique transversal intersection with $L$), then every Fatou component of $f$ in the basin of $L$ is an extension of a one-dimensional Fatou component of $f|_L$. As a corollary, there is no wandering Fatou component. We will also discuss the multicritical case under additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_01715 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The wandering domain problem for attracting polynomial skew products Ji, Zhuchao Shen, Weixiao Dynamical Systems Complex Variables Wandering Fatou components were recently constructed by Astorg et al for higher-dimensional holomorphic maps on projective spaces. Their examples are polynomial skew products with a parabolic invariant line. In this paper, we study this wandering domain problem for polynomial skew product $f$ with an attracting invariant line $L$ (which is the more common case). We show that if $f$ is unicritical (in the sense that the critical curve has a unique transversal intersection with $L$), then every Fatou component of $f$ in the basin of $L$ is an extension of a one-dimensional Fatou component of $f|_L$. As a corollary, there is no wandering Fatou component. We will also discuss the multicritical case under additional assumptions. |
| title | The wandering domain problem for attracting polynomial skew products |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2209.01715 |