Graph maps with zero topological entropy and sequence entropy pairs

Graph maps with zero topological entropy and sequence entropy pairs

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 \omega-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 com...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2021-11, Vol.149 (11), p.4757-4770
Hauptverfasser: Li, Jian, Liang, Xianjuan, Oprocha, Piotr
Format: Artikel
Sprache:eng
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Zusammenfassung: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 \omega-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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/15578