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Equicontinuity and Sensitivity in Mean Forms

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Abstract

In this paper two mean forms of equicontinuity and sensitivity are mainly studied. For the equicontinuity side, it is shown that any topological dynamical system can be embedded into some almost equicontinuous in the mean system. For the sensitivity side, it turns out that the notions of sensitivity in the mean and mean sensitivity are identical in the measure-theoretical setting, though they are different in the topological setting. Moreover, levels of mean multi-variant versions of sensitivity in topological or measure-theoretical sense are completely classified.

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Acknowledgements

The authors thank Jian Li for the useful suggestions. Research of Jie Li is supported by NNSF of China (Grant no. 11701231), NSF of Jiangsu Province (Grant no. BK20170225) and Science Foundation of Jiangsu Normal University (Grant no. 17XLR011). Xiangdong Ye is supported by NNSF of China (Grant no. 12031019), and grants from CAS and Anhui Province. Tao Yu is supported by NNSF of China (Grant No. 12001354).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Jie Li

  2. CAS Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Xiangdong Ye

  3. Department of Mathematics, Shantou University, Shantou, 515063, People’s Republic of China

    Tao Yu

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  1. Jie Li
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  2. Xiangdong Ye
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  3. Tao Yu
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Correspondence to Xiangdong Ye.

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Li, J., Ye, X. & Yu, T. Equicontinuity and Sensitivity in Mean Forms. J Dyn Diff Equat 34, 133–154 (2022). https://doi.org/10.1007/s10884-021-09945-9

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  • DOI: https://doi.org/10.1007/s10884-021-09945-9

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