I have failed to find the topological entropy of dyadic Toeplitz system. Do you know what this entropy is?
Dyadic Toeplitz system is a subshift of $\{0,1\}^{\mathbb{Z}}$, i.e. it is an orbit closure of point $x$ constructed as follows: on every second coordinate we place zero, we get sequence $(...*0*0*0*0*...)$, then instead of every second * we place one, we get $(...010*010*010...)$ and so on. In other words, coordinates of element $x$ can be decomposed into arithmetic progressions, on which $x$ is constant. Thank a lot in advance!
Bonjour, your sequence is the fixed point of the primitive substitution 0-->01, 1-->00 thus its entropy is 0:its number of different words of length $n$ should be bounded by 2n or something like that but it is sublinear as all primitive substitutive sequences. You can find more information in a paper of Cassaigne-Karhumaki:1997 or Koskas:1998.