论文标题
有限类型换档$ \ mathbb {z} $和树的拓扑熵
Topological Entropy for Shifts of Finite Type Over $\mathbb{Z}$ and Trees
论文作者
论文摘要
我们研究了HOM割型的拓扑熵，并表明，尽管拓扑熵并不是一般的换档的共轭不变性，但对于HOM Tree较高的块移动而言，它仍然是不变的。在doi：10.1016/j.tcs.2018.05.034和doi：10.3934/dcds.2020186，Petersen和Salama展示了树木偏移的拓扑熵，$ h（\ Mathcal {\ Mathcal {t} _x _x _x） $ x $。当$ x $是有限类型的变化的情况下，我们表征了必要且充分的条件。此外，已经揭示了两种新型现象。有限类型的HOM换档的拓扑熵有一个差距，这使得不密集。最后但并非最不重要的一点是，有限类型的可还原性HOM迁移的拓扑熵等于或大于其最大不可减至的成分的拓扑熵。
We study the topological entropy of hom tree-shifts and show that, although the topological entropy is not a conjugacy invariant for tree-shifts in general, it remains invariant for hom tree higher block shifts. In doi:10.1016/j.tcs.2018.05.034 and doi:10.3934/dcds.2020186, Petersen and Salama demonstrated the existence of topological entropy for tree-shifts and $h(\mathcal{T}_X) \geq h(X)$, where $\mathcal{T}_X$ is the hom tree-shift derived from $X$. We characterize a necessary and sufficient condition when the equality holds for the case where $X$ is a shift of finite type. In addition, two novel phenomena have been revealed for tree-shifts. There is a gap in the set of topological entropy of hom tree-shifts of finite type, which makes such a set not dense. Last but not least, the topological entropy of a reducible hom tree-shift of finite type is equal to or larger than that of its maximal irreducible component.
