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A twisted tensor product on symbolic dynamical systems and the Ashley's problem
We define the notion of
fiber bundle via a twisted tensor product on the transition matrices.
We define the notion of topological conjugacy and shift equivalence
in this
bundle context and show that topological conjugacy implies shift
equivalence.
We show that the "Ashley system" $\Sigma_A$ fits into
our fiber bundle context. We introduce another system $\Sigma_W$,
topologically
conjugate to the full $2-$shift,
which has the same base space and fiber as the
Ashley system, but is constructed with a different twisting.
We show that
$\Sigma_A$ and $\Sigma_W$ are shift equivalent but not bundle isomorphic.