Abstract
We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle. We construct a weak mixing minimal special flow with bounded topological complexity. We also prove that if the roof function is \(C^\infty \), then the special flow has sub-polynomial topological complexity and the time one map meets the condition of Sarnak’s conjecture.
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Huang is partially supported by NNSF of China (11431012,11731003) and Xu is partially supported by NNSF of China (11801538, 11871188).
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Huang, W., Xu, L. Special Flow, Weak Mixing and Complexity. Commun. Math. Stat. 7, 85–122 (2019). https://doi.org/10.1007/s40304-018-0166-5
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DOI: https://doi.org/10.1007/s40304-018-0166-5