Abstract
Firstly, we introduced the concept of G â Lipschitz tracking property, G â asymptotic average tracking property, and G â periodic tracking property. Secondly, we studied their dynamical properties and topological structure and obtained the following conclusions: (1) let X , d be compact metric G â space and the metric d be invariant to G . Then, Ï has G ÂŻ â asymptotic average tracking property; (2) let X , d be compact metric G â space and the metric d be invariant to G . Then, Ï has G ÂŻ â Lipschitz tracking property; (3) let X , d be compact metric G â space and the metric d be invariant to G . Then, Ï has G ÂŻ â periodic tracking property. The above results make up for the lack of theory of G â Lipschitz tracking property, G â asymptotic average tracking property, and G â periodic tracking property in infinite product space under group action.
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