Complexity and invariant measure of the period-doubling subshift

Miroslava Poláková

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arXiv · 1902.08387

Complexity and invariant measure of the period-doubling subshift

Miroslava Poláková

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Abstract

Explicit formulas for complexity and unique invariant measure of the period-doubling subshift can be derived from those for the Thue-Morse subshift, obtained by Brlek, De Luca and Varricchio, and Dekking. In this note we give direct proofs based on combinatorial properties of the period-doubling sequence. We also derive explicit formulas for correlation integral and other recurrence characteristics of the period-doubling subshift. As a corollary we obtain that the determinism of this subshift converges to 1 as the distance threshold approaches 0.

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Miroslava Poláková. 2019-02-22. Complexity and invariant measure of the period-doubling subshift. https://arxiv.org/abs/1902.08387

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