Symbolic dynamics for certain non-invertible $C^{1+β}$ maps
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915779657596928 |
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| author | Xun, Jing Zhang, Yifan Zhu, Yujun |
| author_facet | Xun, Jing Zhang, Yifan Zhu, Yujun |
| contents | Let $f$ be a non-invertible $C^{1+β}(β>0)$ map with zero Lyapunov exponents and singularities on a closed Riemannian manifold $M$. We consider the symbolic dynamics of $f$. Combining the techniques in recent works of Sarig, Ovadia and Araujo-Lima-Poletti, we construct a countable Markov partition for the invariant set consisting of summable points of the inverse limit space of $(M, f)$ and show that there exists a finite-to-one symbolic extension for $f$ on the corresponding subset of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symbolic dynamics for certain non-invertible $C^{1+β}$ maps Xun, Jing Zhang, Yifan Zhu, Yujun Dynamical Systems Let $f$ be a non-invertible $C^{1+β}(β>0)$ map with zero Lyapunov exponents and singularities on a closed Riemannian manifold $M$. We consider the symbolic dynamics of $f$. Combining the techniques in recent works of Sarig, Ovadia and Araujo-Lima-Poletti, we construct a countable Markov partition for the invariant set consisting of summable points of the inverse limit space of $(M, f)$ and show that there exists a finite-to-one symbolic extension for $f$ on the corresponding subset of $M$. |
| title | Symbolic dynamics for certain non-invertible $C^{1+β}$ maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2602.06354 |