Geodesic
On the entropies of subshifts of finite type on countable amenable groups
Sebastián Barbieri1
1Universidad de Santiago de Chile, Chile
Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 607-638

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DOI

Let G,H be two countable amenable groups. We introduce the notion of group charts, which gives us a tool to embed an arbitrary H-subshift into a G-subshift. Using an entropy addition formula derived from this formalism we prove that whenever H is finitely presented and admits a subshift of finite type (SFT) on which H acts freely, then the set of real numbers attained as topological entropies of H-SFTs is contained in the set of topological entropies of G-SFTs modulo an arbitrarily small additive constant for any finitely generated group G which admits a translation-like action of H. In particular, we show that the set of topological entropies of G-SFTs on any such group which has decidable word problem and admits a translation-like action of Z2 coincides with the set of non-negative upper semi-computable real numbers. We use this result to give a complete characterization of the entropies of SFTs in several classes of groups.
DOI : 10.4171/ggd/608
Classification : 37-XX, 22-XX
Mots-clés : Topological entropy, symbolic dynamics, subshifts of finite type, amenable groups, cocycles of group actions

Sebastián Barbieri  1

1 Universidad de Santiago de Chile, Chile 
Sebastián Barbieri. On the entropies of subshifts of finite type on countable amenable groups. Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 607-638. doi: 10.4171/ggd/608
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     year = {2021},
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     number = {2},
     doi = {10.4171/ggd/608},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/608/}
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