The Chaotic Properties of Increasing Gap Shifts - Nor Syahmina Kamarudin; Malouh Baloush; Syahida Che Dzul-Kifli (International Journal of Mathematics and Mathematical Sciences)
It is well known that locally everywhere onto, totally transitive, and topologically mixing are equivalent on shift of finite type. It turns out that this relation does not hold true on shift of infinite type. We introduce the increasing gap shift and determine its chaotic properties. The increasing gap shift and the sigma star shift serve as counterexamples to show the relation between the three chaos notions on shift of infinite type.