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On Li-Yorke pairs by François Blanchard; Eli Glasner; Sergii Kolyada; Alejandro Maass is a Mathematics article available to read on EtoBox.

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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 su‰cient 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.

Who reads On Li-Yorke pairs?

Author

François Blanchard; Eli Glasner; Sergii Kolyada; Alejandro Maass

Publisher

Walter de Gruyter GmbH

Published

2002

Field

Mathematics (Physical Sciences)