Topological entropy of transitive dendrite maps

TL;DR

This paper demonstrates that certain dendrites can support transitive, chaotic maps with arbitrarily small entropy, addressing a question in topological dynamics and entropy on dendrites.

Contribution

It provides a partial answer to Baldwin's 2001 question by constructing specific chaotic maps on dendrites with minimal entropy.

Findings

Existence of transitive, chaotic maps with arbitrarily small entropy on certain dendrites

Characterization of dendrites that admit such maps

Progress towards understanding entropy bounds in dendrite dynamics

Abstract

We show that every dendrite satisfying the condition that no subtree of it contains all free arcs admits a transitive, even exactly Devaney chaotic map with arbitrarily small entropy. This gives a partial answer to a question of Baldwin from 2001.