The Shadowing Properties Of Nonautonomous Dynamical System
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911810739765248 |
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| author | An, Min |
| author_facet | An, Min |
| contents | Let $\left(X_n, d_n\right)$ be a sequence of metric spaces and let $\mathcal{F}=\left\{f_n\right\}_{n \in \mathbb{Z}}$ be a sequence of continuous and onto maps $f_n: X_n \rightarrow X_{n+1}, n \in \mathbb{Z}_{+}$. In this paper, we prove that if the compression ratio meets $\prod λ_i=0$, then there exists $δ_n>0$ such that any $δ_n$ - pseudo-orbit $\left\{x_n\right\}_{n \in \mathbb{Z}}$ is $\varepsilon$ - shadowed by a unique point $x \in X_0$. For the asymptotic average shadowing property, we prove that if $\left.\mathcal{F}\right|_A$ has asymptotically average shadowing property, then $\mathcal{F}$ also has a asymptotically average shadowing propertywhen a density-related condition is satisfied. Additionally, the conclusion that the shadowing performance of strong equicontinuity and pseudo-shadowing property implies limit shadowing is also obtained. Furthermore, the shadowing property of non-autonomous product space is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Shadowing Properties Of Nonautonomous Dynamical System An, Min Dynamical Systems Let $\left(X_n, d_n\right)$ be a sequence of metric spaces and let $\mathcal{F}=\left\{f_n\right\}_{n \in \mathbb{Z}}$ be a sequence of continuous and onto maps $f_n: X_n \rightarrow X_{n+1}, n \in \mathbb{Z}_{+}$. In this paper, we prove that if the compression ratio meets $\prod λ_i=0$, then there exists $δ_n>0$ such that any $δ_n$ - pseudo-orbit $\left\{x_n\right\}_{n \in \mathbb{Z}}$ is $\varepsilon$ - shadowed by a unique point $x \in X_0$. For the asymptotic average shadowing property, we prove that if $\left.\mathcal{F}\right|_A$ has asymptotically average shadowing property, then $\mathcal{F}$ also has a asymptotically average shadowing propertywhen a density-related condition is satisfied. Additionally, the conclusion that the shadowing performance of strong equicontinuity and pseudo-shadowing property implies limit shadowing is also obtained. Furthermore, the shadowing property of non-autonomous product space is also discussed. |
| title | The Shadowing Properties Of Nonautonomous Dynamical System |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2403.15777 |