Advances on Stable Ergodicity of Toral Automorphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866915889284120576 |
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| author | Argentieri, Fernando Ulliana, Andrea |
| author_facet | Argentieri, Fernando Ulliana, Andrea |
| contents | We prove that all ergodic automorphisms of the $N$-dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension $N\leq 5$ or $N=7$. This generalizes a previous result of Rodriguez-Hertz, that required an additional algebraic condition on the carachteristic polynomial of the linear automorphism. The core of the proof is a minimality criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Advances on Stable Ergodicity of Toral Automorphisms Argentieri, Fernando Ulliana, Andrea Dynamical Systems We prove that all ergodic automorphisms of the $N$-dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension $N\leq 5$ or $N=7$. This generalizes a previous result of Rodriguez-Hertz, that required an additional algebraic condition on the carachteristic polynomial of the linear automorphism. The core of the proof is a minimality criterion. |
| title | Advances on Stable Ergodicity of Toral Automorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.23778 |