Direct topological factorization for topological flows

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3 Scopus citations

Abstract

This paper considers the general question of when a topological action of a countable group can be factored into a direct product of non-trivial actions. In the early 1980s, D. Lind considered such questions for Z-shifts of finite type. In particular, we study direct factorizations of subshifts of finite type over Zd and other groups, and Z-subshifts which are not of finite type. The main results concern direct factors of the multidimensional full n-shift, the multidimensional -colored chessboard and the Dyck shift over a prime alphabet. A direct factorization of an expansive G-action must be finite, but an example is provided of a non-expansive Z-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 G = Z.

Original languageEnglish
Pages (from-to)837-858
Number of pages22
JournalErgodic Theory and Dynamical Systems
Volume37
Issue number3
DOIs
StatePublished - 1 May 2017

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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