Abstract
The dynamical system on \(\mathbb{T}^2\) which is a group extension over an irrational rotation on \(\mathbb{T}^1\) is investigated. The criterion when the extension is minimal, a system of order 2 and when the maximal equicontinuous factor is the irrational rotation is given. The topological complexity of the extension is computed, and a negative answer to the latter part of an open question raised by Host et al. (2014) is obtained.
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Qiao, Y. Topological complexity, minimality and systems of order two on torus. Sci. China Math. 59, 503–514 (2016). https://doi.org/10.1007/s11425-015-5042-0
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DOI: https://doi.org/10.1007/s11425-015-5042-0