Some properties of circle maps with zero topological entropy

Abstract

For a circle map $f:\mathbb{S}\to \mathbb{S}$ with zero topological entropy, we show that a non-diagonal pair $⟨x,y⟩\in \mathbb{S}\times \mathbb{S}$ is non-separable if and only if it is an IN-pair if and only if it is an IT-pair. We also show that if a circle map is topological null then the maximal pattern entropy of every open cover is of polynomial order.

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• Topological entropy of nonautonomous dynamical systems
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• On dynamics of graph maps with zero topological entropy
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