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arXiv · 1108.2354

On the dynamics of subcontinua of a tree

Mykola Matviichuk
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Abstract

Given a tree map $f:T\to T$, we study the dynamics of subcontinua of $T$ under action of $f$. In particular, we prove that a subcontinuum of $T$ is either asymptotically periodic or asymptotically degenerate. As an application of this result, we show that zero topological entropy of the system $(T,f)$ implies zero topological entropy of its functional envelope (endowed with the Hausdorff metric).

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Mykola Matviichuk. 2011-08-11. On the dynamics of subcontinua of a tree. https://doi.org/10.1080/10236198.2011.634804

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