A note about various types of sensitivity in general semiflows

Alica Miller


We discuss the implications between various types of sensitivity in general semiflows (sensitivity, syndetic sensitivity, thick sensitivity, thick syndetic sensitivity, multisensitivity, periodic sensitivity, thick periodic sensitivity), including the weak mixing as a very strong type of sensitivity and the strong mixing as the strongest of all type of sensitivity.


Sensitivity; strong mixing; weak mixing; strong sensitivity; multisensitivity; syndetic sensitivity; thick sensitivity; thick syndetic sensitivity; periodic sensitivity; thick periodic sensitivity

Subject classification

Primary 54H15, 20M20; Secondary 54H20

Full Text:



E. Glasner, Ergodic Theory via Joinings, Mathematical Surveys and Monographs, American Mathematical Society, 2003. https://doi.org/10.1090/surv/101

E. Glasner and D. Maon, Rigidity in topological dynamics, Ergod. Th. & Dynam. Sys.9 (1989), 309-320. https://doi.org/10.1017/S0143385700004983

L. He, X. Yan and L. Wang, Weak-mixing implies sensitive dependence, J. Math. Anal.Appl. 299 (2004), 300-304. https://doi.org/10.1016/j.jmaa.2004.06.066

E. Kontorovich, M. Megrelishvili, A note on sensitivity of semigroup actions, Semigroup Forum 76 (2008), 133-141. https://doi.org/10.1007/s00233-007-9033-5

H. Liu, L. Liao and L. Wang, Thickly syndetical sensitivity of topological dynamical system, Discrete Dyn. Nature Soc. 2014, Article ID 583431. https://doi.org/10.1155/2014/583431

A. Miller, Weak mixing in general semiflows implies multi-sensitivity, but not thick sensitivity, J. Nonlinear Sci. Appl., to appear.

A. Miller and C. Money, Chaos-related properties on the product of semiflows, TurkishJ. Math. 41 (2017), 1323-1336. https://doi.org/10.3906/mat-1612-39

T. S. Moothathu, Stronger forms of sensitivity for dynamical systems, Nonlinaerity 20 (2007), 2115-2126. https://doi.org/10.1088/0951-7715/20/9/006

T. Wang, J. Yin and Q. Yan, The sufficient conditions for dynamical systems of semi-group actions to have some stronger forms of sensitivities, J. Nonlinear Sci. Appl. 9(2016), 989-997. https://doi.org/10.22436/jnsa.009.03.27

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1. Relationship among several types of sensitivity in general semi-flows
Xinxing Wu, Xu Zhang
Semigroup Forum  vol: 101  issue: 1  first page: 226  year: 2020  
doi: 10.1007/s00233-019-10072-7

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Universitat Politècnica de València

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