Formulas for complexity, invariant measure and RQA characteristics of the period-doubling subshift

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 two basic characteristics of recurrence quantification analysis (RQA) of the period-doubling subshift: recurrence rate and determinism. As a corollary we obtain that RQA determinism of this subshift converges to 1 as the threshold distance approaches 0.