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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2312.17447 |
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| _version_ | 1866911743324717056 |
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| author | Gomes, Elena |
| author_facet | Gomes, Elena |
| contents | Let $f$ be a polynomial-like mapping of the sphere of degree $d \geq 2$. We show that the Julia set $J(f)$ of $f$ cannot be the union of a finite number of proper indecomposable subcontinua. As a corollary, we prove that $J(f)$ is an indecomposable continuum if and only if there exists a prime end of some complementary region of $J(f)$ whose impression is the entire $J(f)$, generalizing a result by Childers, Mayer and Rogers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17447 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Indecomposable continua and the Julia sets of polynomial-like mappings Gomes, Elena Dynamical Systems Let $f$ be a polynomial-like mapping of the sphere of degree $d \geq 2$. We show that the Julia set $J(f)$ of $f$ cannot be the union of a finite number of proper indecomposable subcontinua. As a corollary, we prove that $J(f)$ is an indecomposable continuum if and only if there exists a prime end of some complementary region of $J(f)$ whose impression is the entire $J(f)$, generalizing a result by Childers, Mayer and Rogers. |
| title | Indecomposable continua and the Julia sets of polynomial-like mappings |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2312.17447 |