Furstenberg–Ellis–Namioka Structure Theorem on a CHART Group

Original Paper
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Abstract

For \(E({\mathbb {T}})\) being the endomorphism group of the circle group \({\mathbb {T}}\), the Furstenberg–Ellis–Namioka Structure Theorem of the CHART group \(G=E({\mathbb {T}})\times {\mathbb {T}}\) with the product \((f,u)(g,v)=(fg,uvf\circ g(\mathrm{e}^{i}))\) is known to be equal to \(\{G,1_{\mathbb {T}}\times {\mathbb {T}},\{(1_{\mathbb {T}},1)\}\}\). A somewhat similar group structure is known to exist on \(E({\mathbb {T}})\times E({\mathbb {T}})\times {\mathbb {T}}\), studied by Milnes. We give an explicit characterization of the Furstenberg–Ellis–Namioka Structure Theorem for an admissible subgroup \(\Sigma \) of \(E({\mathbb {T}})\times E({\mathbb {T}})\times {\mathbb {T}}\), where \(\Sigma \) is the Ellis group of the Hahn-type skew product dynamical system on the 3-torus \({\mathbb {T}}^3\).

Keywords

Compact right topological group Ellis group Furstenberg–Ellis–Namioka structure theorem 

Mathematics Subject Classification

43A60 

Notes

Acknowledgements

The authors would like to thank the anonymous referee for the kind suggestions. A support from Mahani Mathematical Research Center for the second author is gratefully acknowledged.

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsKerman Branch, Islamic Azad UniversityKermanIran
  2. 2.Department of Pure Mathematics, Faculty of Mathematics and computerShahid Bahonar University of KermanKermanIran

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