Dedicated to Anatole Katok on his 60th birthday. B., Positive algebraic (K)-theory and shifts of finite type, Brin, Michael (ed.) et al., Modern dynamical systems and applications. Lind, Douglas Marcus, Brian, An introduction to symbolic dynamics and coding, ZBL07279890. Edge shifts are the same as vertex shifts are the same as general subshifts of finite type up to topological conjugacy, but I don't know if you can exactly mimic the word counts of a vertex shift with an edge shift all edge shifts can directly be seen as vertex shifts, but not vice versa.) Now the number of admissible words of length $n$ is simply $N_n = |Q^n|_1$, the $1$-norm = sum of entries in the graph. We take $X$ to be the words of exactly length $n$ rather than words of length up to $n$, and by $X^$ edges from vertex $a$ to vertex $b$, and $\Sigma_Q$ is just the bi-infinite paths in this graph. A complete set of computable invariants is given for deciding whether two irreducible subshifts of finite type have topologically equivalent suspension.
If M is primitive, i.e., M > 0 for some positive integer TV, then we say that GIBBS MEASURES 177 (X,5) is amixingsubshift of finite type. Let (X,S)be a subshift of finite type, and letAbe an alphabet for (X,S)with the transition matrix M. Definitions of words used can be found in. subshift (X, 5) is of finite type if and only ifS:X>Xis a local homeomorphism. Let me analyze four interpretations of your construction the first is what I thought first, the second gives something uninteresting, the third gives something uninteresting, the fourth is now my best guess of what you meant (you may want to jump there first to check). A pattern is a function from some nite F Gto A. A subshift of nite type (SFT) is a subset of AGobtained by forbidding (or, equivalently, allowing) some nite set of patterns. So, I probably did not initially understand you correctly. that every topological dynamical system over Gis a factor of a subshift.
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