Author:
Downarowicz Tomasz,Huczek Dawid,Zhang Guohua
Abstract
Abstract
We prove that for any infinite countable amenable group G, any
{\varepsilon>0}
and any finite subset
{K\subset G}
, there exists a tiling (partition of G into finite “tiles” using only finitely many “shapes”), where all the tiles are
{(K,\varepsilon)}
-invariant. Moreover, our tiling has topological entropy zero (i.e., subexponential complexity of patterns). As an application, we construct a free action of G (in the sense that the mappings, associated to elements of G other than the unit, have no fixed points) on a zero-dimensional space, such that the topological entropy of this action is zero.
Funder
Narodowe Centrum Nauki
National Natural Science Foundation of China
Subject
Applied Mathematics,General Mathematics
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