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Complexity and invariant measure of the period-doubling subshift

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arxiv 1902.08387 v1 pith:OSQTHIIY submitted 2019-02-22 math.DS

Miroslava Poláková This is my paper · ORCID
classification math.DS
keywords subshiftperiod-doublingcomplexityexplicitformulasinvariantmeasureapproaches
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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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  1. Exact renormalisation for patch frequencies in inflation systems

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    Exact renormalisation equations yield the relative frequency of any patch in a primitive substitution tiling, with transfer to symbolic and other suspension systems.

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