330 research outputs found
Direct topological factorization for topological flows
This paper considers the general question of when a topological action of a
countable group can be factored into a direct product of a nontrivial actions.
In the early 1980's D. Lind considered such questions for -shifts
of finite type. We study in particular direct factorizations of subshifts of
finite type over and other groups, and -subshifts
which are not of finite type. The main results concern direct factors of the
multidimensional full -shift, the multidimensional -colored chessboard
and the Dyck shift over a prime alphabet.
A direct factorization of an expansive -action must be finite,
but a example is provided of a non-expansive -action for which
there is no finite direct prime factorization. The question about existence of
direct prime factorization of expansive actions remains open, even for
.Comment: 21 pages, some changes and remarks added in response to suggestions
by the referee. To appear in ETD
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