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Symbolic dynamics is the study of dynamical systems defined in terms of shift transformations on spaces of sequences. Examples of topics in this area include shifts of finite type, sofic shifts, Toeplitz shifts, Markov partitions and symbolic coding of dynamical systems.
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probability measures with entropy equal to nonnegative number
There is also a paper of Grillenberger, where You can find the construction http://link.springer.com/article/10.1007%2FBF00537161?LI=true