On the dynamics of subcontinua of a tree
Dynamical Systems
2013-05-30 v1
Abstract
Given a tree map , we study the dynamics of subcontinua of under action of . In particular, we prove that a subcontinuum of is either asymptotically periodic or asymptotically degenerate. As an application of this result, we show that zero topological entropy of the system implies zero topological entropy of its functional envelope (endowed with the Hausdorff metric).
Keywords
Cite
@article{arxiv.1108.2354,
title = {On the dynamics of subcontinua of a tree},
author = {Mykola Matviichuk},
journal= {arXiv preprint arXiv:1108.2354},
year = {2013}
}