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Dynamical quasitilings of amenable group
We prove that for any compact zero-dimensional metric space on which an
infinite countable amenable group acts freely by homeomorphisms, there
exists a dynamical quasitiling with good covering, continuity, F{\o}lner and
dynamical properties, i.e to every we can assign a quasitiling
of (with all the using the same, finite set
of shapes) such that the tiles of are disjoint, their union has
arbitrarily high lower Banach Density, all the shapes of are
large subsets of an arbitrarily large F{\o}lner set, and if we consider
to be an element of a shift space over a certain finite
alphabet, then the mapping is a factor map
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