Quasi-shadowing property for nonuniformly partially hyperbolic systems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929660772745216 |
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| author | Liao, Gang Zu, Xuetong |
| author_facet | Liao, Gang Zu, Xuetong |
| contents | In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+α}$ diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property and quasi-closing property are also investigated. As an application of quasi-closing property, we extend Katok's reslut on the growth of periodoc orbits for hyperbolic ergodic measure to any ergodic measure: the number of quasi-periodic points grows exponentially at least the metric entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-shadowing property for nonuniformly partially hyperbolic systems Liao, Gang Zu, Xuetong Dynamical Systems In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+α}$ diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property and quasi-closing property are also investigated. As an application of quasi-closing property, we extend Katok's reslut on the growth of periodoc orbits for hyperbolic ergodic measure to any ergodic measure: the number of quasi-periodic points grows exponentially at least the metric entropy. |
| title | Quasi-shadowing property for nonuniformly partially hyperbolic systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.03071 |