English

On the dynamics of subcontinua of a tree

Dynamical Systems 2013-05-30 v1

Abstract

Given a tree map f:TTf:T\to T, we study the dynamics of subcontinua of TT under action of ff. In particular, we prove that a subcontinuum of TT is either asymptotically periodic or asymptotically degenerate. As an application of this result, we show that zero topological entropy of the system (T,f)(T,f) 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}
}