Special Flow, Weak Mixing and Complexity

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.

Keywords

Special flow / Weak mixing / Sub-polynomial complexity / Bounded complexity

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