On the dynamics of subcontinua of a tree

Details On the dynamics of subcontinua of a tree On the dynamics of subcontinua of a tree

2011-08-11

arxiv.org/abs/1108.2354v1

Mathematics

Dynamical Systems

Scientific paper

10.1080/10236198.2011.634804

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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