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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09342 |
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Table of 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 $C^ω$.