The research of Lipschitz shadowing property and pointwise periodic shadowing property in nonautonomous dynamical systems
JI Zhanjiang1,2， QIN Guijiang1,2
1.School of Data Science and Software Engineering， Wuzhou University， Wuzhou， Guangxi 543002， China； 2.Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System， Wuzhou University， Wuzhou， Guangxi 543002， China
Abstract：According to the definition of Lipschitz shadowing property and pointwise periodic shadowing property in autonomous dynamical systems， it is introduced that the concept of Lipschitz shadowing property and pointwise periodic shadowing property in nonautonomous dynamical systems， and we study their dynamic properties. The following results are obtained： 1) If F＝{fi}i＝0(∞) and G＝{gi}i＝0(∞)are to be topologically conjugate， then F has Lipschitz shadowing property if and only if G has Lipschitz shadowing property； 2) If F＝{fi}i＝0(∞) and G＝{gi}i＝0(∞) are to be topologically conjugate， then F has pointwise periodic shadowing property if and only if G has pointwise periodic shadowing property； 3) The product system (X×Y，F×G) has Lipschitz shadowing property if and only if (X，F) and (Y，G) have Lipschitz shadowing property. These conclusions make up for the lack of the theory of Lipschitz shadowing property and pointwise periodic shadowing property in autonomous dynamical systems.
冀占江,覃桂茳,. 非自治动力系统中利普希茨跟踪性和逐点周期跟踪性的研究[J]. 华中师范大学学报(自然科学版), 2019, 53(4): 482-486.
JI Zhanjiang,QIN Guijiang,. The research of Lipschitz shadowing property and pointwise periodic shadowing property in nonautonomous dynamical systems. journal1, 2019, 53(4): 482-486.
2019, Vol. 53 
