Sub-shadowings

An extended concept of δδ pseudo-orbit called δδ-ergodic pseudo-orbit is considered. If any δδ-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.