Backward Julia sets for a class of p-adic Hénon like maps
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918217977430016 |
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| author | Bastos, Jéfferson L. R. Caprio, Danilo Raizzaro, Oyran |
| author_facet | Bastos, Jéfferson L. R. Caprio, Danilo Raizzaro, Oyran |
| contents | In this work we study the backward filled Julia sets of a class of $p$-adic polynomial maps $f:\mathbb{Q}_p^2\longrightarrow \mathbb{Q}_p^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{Q}_p$ is a $p$-adic number. In particular, if $|c|\leq 1$, then we proved that the backward filled Julia set of $f$ is a bounded subset in $\mathbb{Z}_p^2$. On the other hand, if $|c|> 1$, then we prove that the backward filled Julia set of $f$ is an unbounded set and has infinity Haar measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Backward Julia sets for a class of p-adic Hénon like maps Bastos, Jéfferson L. R. Caprio, Danilo Raizzaro, Oyran Dynamical Systems 37P40, 11S82, 45M05 In this work we study the backward filled Julia sets of a class of $p$-adic polynomial maps $f:\mathbb{Q}_p^2\longrightarrow \mathbb{Q}_p^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{Q}_p$ is a $p$-adic number. In particular, if $|c|\leq 1$, then we proved that the backward filled Julia set of $f$ is a bounded subset in $\mathbb{Z}_p^2$. On the other hand, if $|c|> 1$, then we prove that the backward filled Julia set of $f$ is an unbounded set and has infinity Haar measure. |
| title | Backward Julia sets for a class of p-adic Hénon like maps |
| topic | Dynamical Systems 37P40, 11S82, 45M05 |
| url | https://arxiv.org/abs/2511.20535 |