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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
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Mixing coded systems and period of their graph presentations
In general no! Let $X=\{0,\,1\}^{\mathbb{Z}}$ be the full shift generated by $\{00,\,10,\,01,\,11\}$ and set $w=12$ and let $\sigma_{X'}$ be the shift map on $X'$. Then $N(w,\,w)=\{n: {\sigma}_{X'}^nw …