Journal of Statistical Physics. Vol. 75. Nos. 3/4. 1994. p. 627-641.
Using the trace mapping and the reduced trace mapping associated with a substitution, one obtaines the spectral properties of one-dimensional Schr6dinger operators of the form H= -d + V on I^2(Z), where d is the discrete Laplacian and V is a diagonal operator with elements derived from a substitution rule. In particular, the reduced trace mapping is closely related to the leading term of the original trace mapping. In this paper, the explicit expression of the leading term is given and its properties are discussed.