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Topological entropies of SFTs in amenable groups

Banff International Research Station for Mathematical Innovation and Discovery

Given a countable amenable group $G$ one can ask which are the real numbers that can be realized as the topological entropy of a subshift of finite type (SFT). A famous result by Hochman and Meyerovitch completely characterizes these numbers for $\mathbb{Z}^2$. I will show that the same characterization is valid for any amenable group with decidable word problem which admits an action of $\mathbb{Z}^2$ which is free and bounded. Using this result we can give a full characterization of the entropies of SFTs for polycyclic groups. Furthermore, the same result holds for any countable group with decidable word problem which contains the direct product of any pair of infinite, finitely generated and amenable groups. In particular, it holds for many branch groups such as the Grigorchuk group.

Mathematics; Dynamical systems and ergodic theory; Group theory and generalizations; Dynamical systems

video/mp4

Author affiliation: University of British Columbia

2019-11-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72239

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/