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Abstract:
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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. |