Limit Bi-Shadowing for Semi-Hyperbolic Systems
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915899849572352 |
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| author | Cheng, Linying Guo, Haiye |
| author_facet | Cheng, Linying Guo, Haiye |
| contents | This paper investigates the shadowing properties in semi-hyperbolic systems. We introduce three classes of shadowing properties defined on families of manifolds, and prove that a semi-hyperbolic family possesses the $L^p$ bi-shadowing property, the limit bi-shadowing property, and the asymptotic bi-shadowing property under certain conditions. The proof strategy is to transform the shadowing problem into a fixed-point problem, and then apply the Brouwer fixed-point theorem to complete the verification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28539 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit Bi-Shadowing for Semi-Hyperbolic Systems Cheng, Linying Guo, Haiye Dynamical Systems This paper investigates the shadowing properties in semi-hyperbolic systems. We introduce three classes of shadowing properties defined on families of manifolds, and prove that a semi-hyperbolic family possesses the $L^p$ bi-shadowing property, the limit bi-shadowing property, and the asymptotic bi-shadowing property under certain conditions. The proof strategy is to transform the shadowing problem into a fixed-point problem, and then apply the Brouwer fixed-point theorem to complete the verification. |
| title | Limit Bi-Shadowing for Semi-Hyperbolic Systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.28539 |