TY - JOUR

T1 - Direct topological factorization for topological flows

AU - Meyerovitch, Tom

N1 - Funding Information:
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 333598 and from the Israel Science Foundation (grant no. 626/14).
Publisher Copyright:
© 2015 Cambridge University Press.

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84948694770&partnerID=8YFLogxK

U2 - 10.1017/etds.2015.67

DO - 10.1017/etds.2015.67

M3 - Article

AN - SCOPUS:84948694770

VL - 37

SP - 837

EP - 858

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 3

ER -