TL;DR
This paper constructs dendrites with endpoint sets matching any totally disconnected compact metric space, enabling the embedding of zero-dimensional systems and addressing chaos-related problems.
Contribution
It introduces a method to embed zero-dimensional dynamical systems into dendrites with specific endpoint sets, solving a longstanding problem in chaos theory.
Findings
Successfully embeds zero-dimensional systems into dendrites
Addresses Li-Yorke and distributional chaos problems
Constructs dendrites with prescribed endpoint sets
Abstract
We construct dendrites with endpoint sets isometric to any totally disconnected compact metric space. This allows us to embed zero-dimensional dynamical systems into dendrites and solve a problem regarding Li-Yorke and distributional chaos.
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