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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.10722 |
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| _version_ | 1866911462041059328 |
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| author | Morelli, Juan C. |
| author_facet | Morelli, Juan C. |
| contents | Given any triplet of positive integers $n \geq 2$, $m$ and $k$ such that $n=m+k$, we exhibit a $C^1$ robustly transitive endomorphism of $\mathbb{T}^n$ with persistent critical points in the isotopy class of $F \times Id$, where $F$ is an expanding map of $\mathbb{T}^m$ and $Id$ is the identity of $\mathbb{T}^k$. Furthermore, if $k$ is small, the map is not only in the isotopy class but in fact a perturbation of $F \times Id$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robustly transitive maps with critical points and large dimensional central spaces Morelli, Juan C. Dynamical Systems Given any triplet of positive integers $n \geq 2$, $m$ and $k$ such that $n=m+k$, we exhibit a $C^1$ robustly transitive endomorphism of $\mathbb{T}^n$ with persistent critical points in the isotopy class of $F \times Id$, where $F$ is an expanding map of $\mathbb{T}^m$ and $Id$ is the identity of $\mathbb{T}^k$. Furthermore, if $k$ is small, the map is not only in the isotopy class but in fact a perturbation of $F \times Id$. |
| title | Robustly transitive maps with critical points and large dimensional central spaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.10722 |