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Boundedness of oriented walks generated by substitutions

F. M. DekkingZ.-Y. Wen — 1996

Journal de théorie des nombres de Bordeaux

Let x = x 0 x 1 be a fixed point of a substitution on the alphabet a , b , and let U a = - 1 - 1 0 1 and U b = 1 1 0 1 . We give a complete classification of the substitutions σ : a , b according to whether the sequence of matrices U x 0 U x 1 U x n n = 0 is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.

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