Quasi-shadowing for partially hyperbolic flows
Quasi-shadowing for partially hyperbolic flows
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部分双曲流的准阴影
DOI：
10.3934/dcds.2020107
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发表时间：
2020
影响因子：
1.1
通讯作者：
Zhou Yunhua
中科院分区：
文献类型：
--
作者：
Li Zhiping;Zhou Yunhua
In this paper, we study the quasi-shadowing property for partially hyperbolic flows. A partially hyperbolic flow \begin{document}$ \varphi_{t} $\end{document} has the quasi-shadowing property if for any \begin{document}$ (\delta,T) $\end{document} -pseudoorbit \begin{document}$ g(t) $\end{document} of \begin{document}$ \varphi_{t} $\end{document} there exist a sequence of points \begin{document}$ \{y_{k}\}_{k\in\mathbb{Z}} $\end{document} and a reparametrization \begin{document}$ \alpha $\end{document} such that \begin{document}$ \varphi_{\alpha(t)-\alpha(kT)}(y_k) $\end{document} trace \begin{document}$ g(t) $\end{document} in which \begin{document}$ y_{k} $\end{document} is obtained from \begin{document}$ \varphi_{\alpha(kT)-\alpha((k-1)T)}(y_{k-1}) $\end{document} by a motion along the central direction. We prove that any partially hyperbolic flow \begin{document}$ \varphi_{t} $\end{document} has the quasi-shadowing property. We also investigate the limit quasi-shadowing properties for flows. That is, a partially hyperbolic flow has the \begin{document}$ \mathcal{L}^p $\end{document} , limit and asymptotic quasi-shadowing properties.
In this paper, we study the quasi-shadowing property for partially hyperbolic flows. A partially hyperbolic flow \begin{document}$ \varphi_{t} $\end{document} has the quasi-shadowing property if for any \begin{document}$ (\delta,T) $\end{document} -pseudoorbit \begin{document}$ g(t) $\end{document} of \begin{document}$ \varphi_{t} $\end{document} there exist a sequence of points \begin{document}$ \{y_{k}\}_{k\in\mathbb{Z}} $\end{document} and a reparametrization \begin{document}$ \alpha $\end{document} such that \begin{document}$ \varphi_{\alpha(t)-\alpha(kT)}(y_k) $\end{document} trace \begin{document}$ g(t) $\end{document} in which \begin{document}$ y_{k} $\end{document} is obtained from \begin{document}$ \varphi_{\alpha(kT)-\alpha((k-1)T)}(y_{k-1}) $\end{document} by a motion along the central direction. We prove that any partially hyperbolic flow \begin{document}$ \varphi_{t} $\end{document} has the quasi-shadowing property. We also investigate the limit quasi-shadowing properties for flows. That is, a partially hyperbolic flow has the \begin{document}$ \mathcal{L}^p $\end{document} , limit and asymptotic quasi-shadowing properties.
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DOI：
10.1007/bfb0093184
发表时间：
1999
期刊：
--
影响因子：
--
作者：
S. Pilyugin
通讯作者：
S. Pilyugin
DOI：
10.1090/s0002-9947-08-04743-0
发表时间：
2007-10
影响因子：
1.3
作者：
Wenxiang Sun;T. Young;Yunhua Zhou
通讯作者：
Wenxiang Sun;T. Young;Yunhua Zhou
影响因子：
0.9
作者：
Y. Sinai
通讯作者：
Y. Sinai
影响因子：
1.1
作者：
Shaobo Gan
通讯作者：
Shaobo Gan
DOI：
10.1007/bfb0076829
发表时间：
2007
期刊：
--
影响因子：
--
作者：
Steven Finch
通讯作者：
Steven Finch