The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities

Volume 9, Issue 3, pp 989--997 http://dx.doi.org/10.22436/jnsa.009.03.27

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Authors

Tao Wang - Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China. Jiandong Yin - Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China. Qi Yan - Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China.

Abstract

In this paper, we introduce several stronger forms of sensitivities in the dynamical systems of semigroup actions, such as thick sensitivity and thickly syndetical sensitivity, and obtain some sufficient conditions for a dynamical system to have such sensitivities. We prove that a weakly mixing system of semigroup actions is thickly sensitive and a minimal weakly mixing system as well as a nonminimal M-system of semigroup actions is thickly syndetically sensitive.

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ISRP Style

Tao Wang, Jiandong Yin, Qi Yan, The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 989--997

AMA Style

Wang Tao, Yin Jiandong, Yan Qi, The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities. J. Nonlinear Sci. Appl. (2016); 9(3):989--997

Chicago/Turabian Style

Wang, Tao, Yin, Jiandong, Yan, Qi. "The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 989--997

Keywords

Semigroup action
thick sensitivity
thickly syndetical sensitivity
weakly mixing.

MSC

54H20
37D45

References

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