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

H. M. Hastings; S. Silberger; M. T. Weiss; Y. Wu

doi:10.3934/dcds.2003.9.549

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2003, Volume 9, Issue 3: 549-558. Doi: 10.3934/dcds.2003.9.549

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

1.
Department of Mathematics, Hofstra University, Hempstead, NY 11550

Received: January 31, 2002

Revised: October 31, 2002

Published: April 2003

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Abstract

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.

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Mathematics Subject Classification: Primary: 37B10, 37C15.

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