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The Chaotic Properties of Increasing Gap Shifts

Author

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  • Nor Syahmina Kamarudin
  • Malouh Baloush
  • Syahida Che Dzul-Kifli

Abstract

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.

Suggested Citation

  • Nor Syahmina Kamarudin & Malouh Baloush & Syahida Che Dzul-Kifli, 2019. "The Chaotic Properties of Increasing Gap Shifts," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-5, February.
    • Handle: RePEc:hin:jijmms:2936560
    DOI: 10.1155/2019/2936560
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