Hokkaido Mathematical Journal

Hokkaido Mathematical Journal, 40 (2011) pp.279-312

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Abstract

The notion of substitutions of some primitive components is introduced. A bilateral subshift arising from a substitution of some primitive components is decomposed into pairwise disjoint, locally compact, shift-invariant sets, on each of which an invariant Radon measure is unique up to scaling. In terms of eigenvalues of an incidence matrix associated with the substitution, it is completely characterized when the unique invariant measure is finite.

MSC(Primary) 37B10 68R15, 37A05 non-primitive substitution, subshift, invariant measure, ergodicity