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a b s t r a c tAn 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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A generalization of Run-length-limited (RLL) codes has been introduced and its dynamical properties as a symbolic dynamical system under the shift map will be investigated. A formula for entropy and zeta function will be given and when our system is shift of finite type, its Bowen-Franks groups are obtained.