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Dynamics and Topology of S-gap Shifts
Let and let
and where . In this note, we
show that an -gap shift is subshift of finite type (SFT) if and only if
is finite or cofinite, is almost-finite-type (AFT) if and only if
is eventually constant and is sofic if and only if is eventually
periodic. We also show that there is a one-to-one correspondence between the
set of all -gap shifts and up to conjugacy. This enables us to induce
a topology and measure structure on the set of all -gaps. By using this, we
give the frequency of certain -gap shifts with respect to their dynamical
properties.Comment: This paper has been withdrawn due to a flaw in Theorem 3.2. The
correct version with some minor results will be replace
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