PROJECTIONAL ENTROPY AND THE ELECTRICAL WIRE SHIFT

Abstract

In this paper we present an extendible, block gluing Z3 shift of finite type Wel in which the topological entropy equals the L-projectional entropy for a two-dimensional sublattice L Z3, even so Wel is not a full Z extension of Wel L . In particular this example shows that Theorem 4.1 of [4] 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 Zd shifts – instead of shifts of finite type – under the same mixing assumption as in [4] and by posing a stronger mixing condition we also obtain the corresponding statement for higher-dimensional sublattices.