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Thickly Syndetical Sensitivity of Topological Dynamical System

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  • Heng Liu
  • Li Liao
  • Lidong Wang

Abstract

Consider the surjective continuous map , where is a compact metric space. In this paper we give several stronger versions of sensitivity, such as thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, and strong sensitivity. We establish the following. (1) If is minimal and sensitive, then is syndetically sensitive. (2) Weak mixing implies thick sensitivity. (3) If is minimal and weakly mixing, then it is thickly syndetically sensitive. (4) If is a nonminimal -system, then it is thickly syndetically sensitive. Devaney chaos implies thickly periodic sensitivity. (5) We give a syndetically sensitive system which is not thickly sensitive. (6) We give thickly syndetically sensitive examples but not cofinitely sensitive ones.

Suggested Citation

  • Heng Liu & Li Liao & Lidong Wang, 2014. "Thickly Syndetical Sensitivity of Topological Dynamical System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-4, April.
    • Handle: RePEc:hin:jnddns:583431
    DOI: 10.1155/2014/583431
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    Cited by:

    1. Salman, Mohammad & Das, Ruchi, 2018. "Multi-sensitivity and other stronger forms of sensitivity in non-autonomous discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 341-348.

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