On the stability and shadowing of tree-shifts of finite type

Dawid Bucki

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arXiv · 2403.04456

On the stability and shadowing of tree-shifts of finite type

Dawid Bucki

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Abstract

We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that the tree-shift is topologically stable and all shift maps are open. We also present an example of a tree-shift for which all shift maps are open but which is not of finite type. It also turns out, that if a topologically stable tree-shift does not have isolated points then it is of finite type.

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Dawid Bucki. 2024-03-07. On the stability and shadowing of tree-shifts of finite type. https://arxiv.org/abs/2403.04456

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