Graph maps with zero topological entropy and sequence entropy pairs
Jian Li, Xianjuan Liang, Piotr Oprocha

TL;DR
This paper characterizes when graph maps with zero topological entropy exhibit Li-Yorke chaos, linking non-separable pairs, IN-pairs, and IT-pairs within solenoidal omega-limit sets, thus completing the understanding of sequence entropy in this context.
Contribution
It provides a complete characterization of zero topological sequence entropy for graph maps, connecting various types of pairs and chaos.
Findings
Graph maps with zero topological entropy are Li-Yorke chaotic iff they have an NS-pair.
Non-diagonal pairs are equivalent to NS-pairs, IN-pairs, and IT-pairs in this setting.
The characterization completes the understanding of sequence entropy for graph maps.
Abstract
We show that graph map with zero topological entropy is Li-Yorke chaotic if and only if it has an NS-pair (a pair of non-separable points containing in a same solenoidal -limit set), and a non-diagonal pair is an NS-pair if and only if it is an IN-pair if and only if it is an IT-pair. This completes characterization of zero topological sequence entropy for graph maps.
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