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The Topological Sensitivity with respect to Furstenberg Families

Author

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  • Tengfei Wang
  • Kai Jing
  • Jiandong Yin

Abstract

In this work, a dynamical system means that is a topological space and is a continuous map. The aim of the article is to introduce the conceptions of topological sensitivity with respect to Furstenberg families, - topological sensitivity, and multisensitivity and present some of their basic features and sufficient conditions for a dynamical system to possess some sensitivities. Actually, it is proved that every topologically ergodic but nonminimal system is syndetically sensitive and a weakly mixing system is - thickly topologically sensitive and multisensitive under the assumption that admits some separability.

Suggested Citation

  • Tengfei Wang & Kai Jing & Jiandong Yin, 2020. "The Topological Sensitivity with respect to Furstenberg Families," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-10, June.
    • Handle: RePEc:hin:jnddns:7684072
    DOI: 10.1155/2020/7684072
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