Technical Developments of DA on $\mathbb{T}^3$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916951972904960 |
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| author | Zhang, Hangyue |
| author_facet | Zhang, Hangyue |
| contents | We constructed a DA on $\mathbb{T}^3$, which complements the work of Gan, Li, Viana, and Yang (\cite{GanLiVianaYang2021}) by providing an example of a $C^\infty$-diffeomorphism with partial volume expansion, where $\dim(E^{cs}) = 2$. In contrast to their work, in \cite{GanLiVianaYang2021}, they provided an example of a non-invertible embedding in the case $\dim(E^{cs}) = 2$. The inverse map of the DA we constructed has a mostly expanding center (\cite{AnderssonVasquez2018}). Using a similar approach, we can also construct a (nontrivial) mixed center (\cite{MiCaoYang2017, MiCao2021}). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_04634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Technical Developments of DA on $\mathbb{T}^3$ Zhang, Hangyue Dynamical Systems 37D30, 37C40, 37D25 We constructed a DA on $\mathbb{T}^3$, which complements the work of Gan, Li, Viana, and Yang (\cite{GanLiVianaYang2021}) by providing an example of a $C^\infty$-diffeomorphism with partial volume expansion, where $\dim(E^{cs}) = 2$. In contrast to their work, in \cite{GanLiVianaYang2021}, they provided an example of a non-invertible embedding in the case $\dim(E^{cs}) = 2$. The inverse map of the DA we constructed has a mostly expanding center (\cite{AnderssonVasquez2018}). Using a similar approach, we can also construct a (nontrivial) mixed center (\cite{MiCaoYang2017, MiCao2021}). |
| title | Technical Developments of DA on $\mathbb{T}^3$ |
| topic | Dynamical Systems 37D30, 37C40, 37D25 |
| url | https://arxiv.org/abs/2509.04634 |