The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos
Volume 82 / 2003
Annales Polonici Mathematici 82 (2003), 265-272
MSC: 37B10, 37B40, 74H65, 34C28, 54H20.
DOI: 10.4064/ap82-3-7
Abstract
We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.
