Projectional entropy and the electrical wire shift

2009/01/16 by Michael H. Schraudner, Schraudner, Michael H.
Mathematics · #37B10 #37B40 #37B50 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #math.CO #math.DS #math.GN #msc:37B10 #msc:37B40 #msc:37B50

paper · pdf · doi:10.48550/arxiv.0901.2494

12 pages, 3 figures

arxiv created 2009/01/16 · arxiv updated 2009/12/01

Abstract

In this paper we present an extendible, block gluing \mathbb Z³ shift of finite type W^el in which the topological entropy equals the L-projectional entropy for a two-dimensional sublattice L:=\mathbb Z e₁+\mathbb Ze₂\subsetneq\mathbb Z³, even so W^el is not a full \mathbb 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 one-dimensional sublattices for general (non-SFT) \mathbb Z^d 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.

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