Geodesic
A characterization of the entropies of multidimensional shifts of finite type
Michael Hochman1 ; Tom Meyerovitch2
1Department of Mathematics<br/>Princeton University<br/>Fine Hall - Washington Rd.<br/>Princeton, NJ<br/>United States<br/>and <br/>School of Mathematics<br/>Institute for Advanced Study<br/>Einstein Dr.<br/>Princeton, NJ 08540<br/>United States
2School of Mathematical Sciences<br/>Tel Aviv University<br/>Ramat Aviv<br/>Tel Aviv 69978<br/>Israel
Annals of mathematics, Tome 171 (2010) no. 3, pp. 2011-2038
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We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number $h\geq0$ is the entropy of such an SFT if and only if it is right recursively enumerable, i.e. there is a computable sequence of rational numbers converging to $h$ from above. The same characterization holds for the entropies of sofic shifts. On the other hand, the entropy of strongly irreducible SFTs is computable.

DOI : 10.4007/annals.2010.171.2011

Michael Hochman  1   ; Tom Meyerovitch  2

1 Department of Mathematics<br/>Princeton University<br/>Fine Hall - Washington Rd.<br/>Princeton, NJ<br/>United States<br/>and <br/>School of Mathematics<br/>Institute for Advanced Study<br/>Einstein Dr.<br/>Princeton, NJ 08540<br/>United States
2 School of Mathematical Sciences<br/>Tel Aviv University<br/>Ramat Aviv<br/>Tel Aviv 69978<br/>Israel 
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Michael Hochman; Tom Meyerovitch. A characterization of the entropies of multidimensional shifts of finite type. Annals of mathematics, Tome 171 (2010) no. 3, pp. 2011-2038. doi: 10.4007/annals.2010.171.2011

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