A non-PI minimal system is Li-Yorke sensitive
Song Shao, Xiangdong Ye
TL;DR
The paper proves that all non-PI minimal systems exhibit Li-Yorke sensitivity, resolving an open question and extending the understanding of chaos in minimal dynamical systems.
Contribution
It establishes that any non-PI minimal system is Li-Yorke sensitive, providing a significant link between non-PI structure and chaotic behavior in minimal systems.
Findings
Non-PI minimal systems are Li-Yorke sensitive
Minimal systems with nontrivial weakly mixing factors are Li-Yorke sensitive
Answers an open question by Akin and Kolyada
Abstract
It is shown that any non-PI minimal system is Li-Yorke sensitive. Consequently, any minimal system with nontrivial weakly mixing factor (such a system is non-PI) is Li-Yorke sensitive, which answers affirmatively an open question by Akin and Kolyada.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · semigroups and automata theory