Li-Yorke chaos for ultragraph shift spaces (Q1988318)

In the present paper the authors define a metric structure for the topology of ultragraph shift spaces. The following statement summarizes the chaos-type results in such spaces. Theorem. Let \(\mathcal{G}\) be an ultragraph and \(X\) be the associated shift space. The following statements are equivalent: 1) \(\mathcal{G}\) has a vertex \(v\) such that \(\#CP_{\mathcal{G}}(v)\ge 2\) ; 2) \(X\) has a scrambled pair formed by infinite paths; 3) \(X\) has an uncountable scrambled set which is perfect and compact; 4) \(X\) is Li-Yorke chaotic.