2019/02/22 by Poláková, Miroslava
#37B10 (Primary) 37A35 #68R15 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.08387
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.