On the dynamics of subcontinua of a tree

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).

Cited by in corpus (4)

• On recurrence and entropy in hyperspace of continua in dimension one
• Entropy of induced maps of regular curves homeomorphisms
• Ergodicity of iterated function systems via minimality on the hyper spaces
• On limit sets and equicontinuity in the hyperspace of continua in dimension one