Furstenberg families and chaos on uniform limit maps

Volume 10, Issue 2, pp 805--816 http://dx.doi.org/10.22436/jnsa.010.02.40

Publication Date: February 20, 2017 Submission Date: November 18, 2016

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Authors

Risong Li - School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People’s Republic of China. Yu Zhao - School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People’s Republic of China. Hongqing Wang - School of Science, Guangdong Ocean University, Zhanjiang, Guangdong, 524025, People’s Republic of China.

Abstract

Let (\(f_n\)) be a given sequence of continuous selfmaps of a compact metric space \(X\) which converges uniformly to a continuous selfmap \(f\) of a compact metric space \(X\), and let \(F, F_1\), and \(F_2\) be given Furstenberg families. In this paper, we obtain an equivalence condition for the uniform limit map \(f\) to be \(F\)-transitive or weakly \(F\)-sensitive or \(F\)-sensitive or \((F_1, F_2)\)-sensitive and a necessary condition for the uniform limit map \(f\) to be weakly \(F\)-sensitive or \(F\)-sensitive or \((F_1, F_2)\)-sensitive. Our results extend and improve some existing ones.

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ISRP Style

Risong Li, Yu Zhao, Hongqing Wang, Furstenberg families and chaos on uniform limit maps, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 805--816

AMA Style

Li Risong, Zhao Yu, Wang Hongqing, Furstenberg families and chaos on uniform limit maps. J. Nonlinear Sci. Appl. (2017); 10(2):805--816

Chicago/Turabian Style

Li, Risong, Zhao, Yu, Wang, Hongqing. "Furstenberg families and chaos on uniform limit maps." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 805--816

Keywords

Furstenberg families
transitivity
F-transitivity
sensitivity
weak F-sensitivity
F-sensitivity
\((F_1،F_2)\)-sensitivity

MSC

37B10
37C20
37C50

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