Projectional Entropy and the Electrical Wire Shift – Preliminary Version

In this paper we present an extendible, block gluing Z shift of finite type W el in which the topological entropy equals the L-projectional entropy for a two-dimensional sublattice L ( Z, even so W el is not a full Z extension of W el L . In particular this example shows that Theorem 4.1 of [3] does not generalize to r-dimensional sublattices L for r > 1. Nevertheless we are able to reprove and extend the result about onedimensional sublattices for general Z shifts under the same mixing assumption as in [3] and by posing a stronger mixing condition we also obtain the corresponding statement for higher-dimensional sublattices.