TY - JOUR
T1 - Singular substitutions of constant length
AU - Berlinkov, Artemi
AU - Solomyak, Boris
N1 - Publisher Copyright:
© Cambridge University Press, 2018.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - We consider primitive aperiodic substitutions of constant length and prove that, in order to have a Lebesgue component in the spectrum of the associated dynamical system, it is necessary that one of the eigenvalues of the substitution matrix equals in absolute value. The proof is based on results of Queffélec combined with estimates of the local dimension of the spectral measure at zero.
AB - We consider primitive aperiodic substitutions of constant length and prove that, in order to have a Lebesgue component in the spectrum of the associated dynamical system, it is necessary that one of the eigenvalues of the substitution matrix equals in absolute value. The proof is based on results of Queffélec combined with estimates of the local dimension of the spectral measure at zero.
UR - http://www.scopus.com/inward/record.url?scp=85041581937&partnerID=8YFLogxK
U2 - 10.1017/etds.2017.133
DO - 10.1017/etds.2017.133
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AN - SCOPUS:85041581937
SN - 0143-3857
VL - 39
SP - 2384
EP - 2402
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 9
ER -