By using the properties between the mapf in metric G-space and induced map(f)in orbital space,the dynamical relationship between G-Lipschitz shadowing property,G-equicontinuity,G-non-wandering point of the mapf and Lipschitz shadowing property,equicontinuity,non-wandering point of the induced map(f)are studied.The following conclusions are obtained:(1)The map f has G-Lipschitz shadowing property if and only if the in-duced map(f)has Lipschitz shadowing property.(2)The map f is G-equicontinuous if and only if the induced map(f)is equicontinuous.(3)The G-non-wandering point set ΩG(f)of the map f is dense in X if and only if the non-wandering point set Ω((f))of the induced map(f)is dense in X/G.
关键词
G-利普希茨跟踪性/G-等度连续/G-非游荡点/轨道空间
Key words
G-Lipschitz shadowing property/G-equicontinuity/G-non-wandering point/orbit space
维普
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