In a previous paper ("A characterization of topologically completely positiveentropy for shifts of finite type"), the author gave a characterization forwhen a $\mathbb{Z}^d$-shift of finite type (SFT) has no nontrivial subshiftfactors with zero entropy, a property which we here call zero-dimensionaltopologically completely positive entropy (ZTCPE). In this work, we study thedifference between this notion and the more classical topologically completelypositive entropy (TCPE) of Blanchard. We show that there are one-dimensionalsubshifts and two-dimensional SFTs which have ZTCPE but not TCPE. In addition,we show that strengthening the hypotheses of the main result of theaforementioned paper yields a sufficient condition for a $\mathbb{Z}^d$-SFT tohave TCPE.
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机译：在先前的论文（“有限类型移位的拓扑完全正熵的表征”）中，作者给出了当$ \ mathbb {Z} ^ d $有限类型移位（SFT）不具有零的非平凡子移位因子时的特征熵，在这里我们称之为零维拓扑完全正熵（ZTCPE）。在这项工作中，我们研究了这一概念与布兰查德（Blanchard）更经典的拓扑完全正熵（TCPE）之间的区别。我们显示存在具有ZTCPE但没有TCPE的一维子移位和二维SFT。此外，我们证明，加强上述论文主要结果的假设为$ \ mathbb {Z} ^ d $ -SFT具有TCPE提供了充分的条件。
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