Projectional entropy and the electrical wire shift

Simple item page
dc.creatorSchraudner, Michael H.
dc.date2009-01-16
dc.date.accessioned2026-07-07T12:31:05Z
dc.date.available2026-07-07T12:31:05Z
dc.descriptionIn this paper we present an extendible, block gluing $\mathbb Z^3$ shift of finite type $W^{\text{el}}$ in which the topological entropy equals the $L$-projectional entropy for a two-dimensional sublattice $L:=\mathbb Z \vec{e}_1+\mathbb Z\vec{e}_2\subsetneq\mathbb Z^3$, even so $W^{\text{el}}$ is not a full $\mathbb Z$ extension of $W^{\text{el}}_L$. 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.
dc.description12 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0901.2494
dc.identifierhttp://arxiv.org/abs/0901.2494
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216334
dc.subjectDynamical Systems
dc.subjectCombinatorics
dc.subjectGeneral Topology
dc.subject37B50, 37B10, 37B40
dc.titleProjectional entropy and the electrical wire shift
dc.typetext

Files

Collections

arXiv