Derived from expanding endomorphism on $\mathbb{T}^2$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912232769585152 |
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| author | Yu, Daohua |
| author_facet | Yu, Daohua |
| contents | Assume that $f$ is a $C^r(r\geq 3)$ specially partially hyperbolic endomorphism on the 2-torus which is homotopic to an expanding linear endomorphism $A$ with irrational eigenvalues. We prove that $f$ and $A$ are topologically conjugate, if and only if $f$ is area-expanding. If $f$ is area-expanding and the center bundle is $C^1$, then the topological conjugacy between $f$ and $A$ is $C^{\max\{r-3,1\}+α}$. In particular, if $r=ω$, the conjugacy is $C^ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derived from expanding endomorphism on $\mathbb{T}^2$ Yu, Daohua Dynamical Systems Assume that $f$ is a $C^r(r\geq 3)$ specially partially hyperbolic endomorphism on the 2-torus which is homotopic to an expanding linear endomorphism $A$ with irrational eigenvalues. We prove that $f$ and $A$ are topologically conjugate, if and only if $f$ is area-expanding. If $f$ is area-expanding and the center bundle is $C^1$, then the topological conjugacy between $f$ and $A$ is $C^{\max\{r-3,1\}+α}$. In particular, if $r=ω$, the conjugacy is $C^ω$. |
| title | Derived from expanding endomorphism on $\mathbb{T}^2$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.09342 |