# American Institute of Mathematical Sciences

May  2003, 9(3): 549-558. doi: 10.3934/dcds.2003.9.549

## A twisted tensor product on symbolic dynamical systems and the Ashley's problem

 1 Department of Mathematics, Hofstra University, Hempstead, NY 11550, United States, United States, United States, United States

Received  February 2002 Revised  November 2002 Published  February 2003

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.
Citation: H. M. Hastings, S. Silberger, M. T. Weiss, Y. Wu. A twisted tensor product on symbolic dynamical systems and the Ashley's problem. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 549-558. doi: 10.3934/dcds.2003.9.549
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