Orbits Inside Basins of Attraction of Skew Products
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916722558107648 |
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| author | Fornaess, John Erik Hu, Mi |
| author_facet | Fornaess, John Erik Hu, Mi |
| contents | A basic problem in complex dynamics is to understand orbits of holomorphic maps. One problem is to understand the collection of points $S$ in an attracting basin whose forward orbits land exactly on the attracting fixed point. In the paper [13], the second author showed that for holomorphic polynomials in $\mathbb C$, there is a constant $C$ so that all Kobayashi discs of radius $C$ must intersect this set $S$. In the paper [15], the second author showed that there are holomorphic skew products in $\mathbb {C}^2$ where this result fails. The main result of this paper is to show that for a large class of polynomial skew products, this result nevertheless holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbits Inside Basins of Attraction of Skew Products Fornaess, John Erik Hu, Mi Dynamical Systems A basic problem in complex dynamics is to understand orbits of holomorphic maps. One problem is to understand the collection of points $S$ in an attracting basin whose forward orbits land exactly on the attracting fixed point. In the paper [13], the second author showed that for holomorphic polynomials in $\mathbb C$, there is a constant $C$ so that all Kobayashi discs of radius $C$ must intersect this set $S$. In the paper [15], the second author showed that there are holomorphic skew products in $\mathbb {C}^2$ where this result fails. The main result of this paper is to show that for a large class of polynomial skew products, this result nevertheless holds. |
| title | Orbits Inside Basins of Attraction of Skew Products |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2505.03503 |