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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.19665 |
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| _version_ | 1866917839220244480 |
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| author | Yu, Daohua Gan, Shaobo |
| author_facet | Yu, Daohua Gan, Shaobo |
| contents | We prove that any ergodic endomorphism on torus admits a sequence of periodic orbits uniformly distributed in the metric sense. As a corollary, an endomorphism on torus is ergodic if and only if the Haar measure can be approximated by periodic measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformly distributed periodic orbits of endomorphisms on $n$-tori Yu, Daohua Gan, Shaobo Dynamical Systems We prove that any ergodic endomorphism on torus admits a sequence of periodic orbits uniformly distributed in the metric sense. As a corollary, an endomorphism on torus is ergodic if and only if the Haar measure can be approximated by periodic measures. |
| title | Uniformly distributed periodic orbits of endomorphisms on $n$-tori |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2407.19665 |