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An extended concept of δ pseudo-orbit called δ-ergodic pseudo-orbit is considered. If any δ-ergodic pseudo-orbit of a system is shadowed by a point along a set of positive lower density then we show that this system is chain mixing and if it is minimal then it is topologically weakly mixing and so has Li–Yorke Chaos. A SFT has this property if and only if it is mixing.
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