Abstract
The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is considered in the setting of general topological dynamics. We adopt two opposite points of view. On the one hand sufficient conditions for Li–Yorke chaos in a topological dynamical system are given. We solve a long–standing open question by proving that positive entropy implies Li–Yorke chaos. On the other hand properties of dynamical systems without Li–Yorke pairs are investigated; in addition to having entropy 0, they are minimal when transitive, and the property is stable under factor maps, arbitrary products and inverse limits. Finally it is proved that minimal systems without Li–Yorke pairs are disjoint from scattering systems.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
