Topological quasi-group shifts

Marcelo Sobottka

doi:10.3934/dcds.2007.17.77

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2007, Volume 17, Issue 1: 77-93. Doi: 10.3934/dcds.2007.17.77

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Topological quasi-group shifts

Marcelo Sobottka^1,

1.
Centro de Modelamiento Matemático, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170/3-Correo 3, Santiago

Received: September 30, 2005

Revised: March 31, 2006

Published: December 2006

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Abstract

In this work we characterize those shift spaces which can support a 1-block quasi-group operation and show the analogous of Kitchens result: any such shift is conjugated to a product of a full shift with a finite shift. Moreover, we prove that every expansive automorphism on a compact zero-dimensional quasi-group that verifies the medial property, commutativity and has period 2, is isomorphic to the shift map on a product of a finite quasi-group with a full shift.

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Mathematics Subject Classification: Primary: 37B10, 68P30; Secondary: 20N05, 94A55.

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