orbital shadowing for $3$-flows

GAN Shaobo; LI Ming

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orbital shadowing for $3$-flows

GAN Shaobo 1,LI Ming 2 *

1.LMAM and School of Mathematical Sciences, Peking University, Beijing 100871

2.School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071

*Correspondence author

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Funding: 973 project （No.2011CB808002）, National Science Foundation of China （No.11201244）, National Science Foundation of China (11025101 and11231001); Specialized Research Fund for the Doctoral Program of Higher Education of China （No.20120031120024）

Opened online: 7 January 2016

Accepted by: none

Citation: GAN Shaobo,LI Ming.orbital shadowing for $3$-flows[OL]. [ 7 January 2016] http://en.paper.edu.cn/en_releasepaper/content/4673510

It is called that a flow has the orbital shadowing propertyif for any $arepsilon>0$ there is $d>0$ such that, for any $d$-pseudoorbit $g(t)$ there exists an orbit $Orb(x)$ satisfying $dh(overline{g(t)},overline{Orb(x)})<arepsilon$. In this paper, it shows that the $C^1$-interior of the set of $3$-dimensional flows having the orbital shadowing property is contained in the set of $Omega$-stable $3$-flows.

Keywords:pure mathematics; $3$-flows; orbital shadowing; $Omega$-stability.

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