# Furstenberg families and chaos on uniform limit maps

Volume 10, Issue 2, pp 805--816
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.

### Share and Cite

##### 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

•  37B10
•  37C20
•  37C50

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